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    NCERT Solutions for Class 12 Physics Chapter 13 Nuclei

    Edited By Vishal kumar | Updated on Sep 13, 2023 08:46 AM IST | #CBSE Class 12th

    NCERT Solutions for Class 12 Physics Chapter 13 – Access and Download Free PDF

    NCERT Solutions for Class 12 Physics Chapter 13 Nuclei serve as a crucial resource for achieving high scores in both board exams and competitive ones like JEE and NEET. On this NCERT solution page, you'll discover comprehensive and detailed class 12 nuclei ncert solutions to the entire exercise, ranging from questions 13.1 to 13.22 (exercise questions) and 13.23 to 13.31 (additional exercise questions). Additionally, these class 12 physics chapter 13 exercise solutions are conveniently available in PDF format, allowing students to access them offline, free from any internet constraints.

    Do you know that the size of an atom is 10,000 times the size of a nucleus? But the nucleus contains 99.9% of the mass of an atom. We know that an atom has a structure. Does the nucleus also have a structure? If so what are the constituents and how they are arranged? All these questions are answered in Nuclei Class 12 NCERT text book.

    Nuclei Class 12 chapter comes under modern Physics and you can expect at least one question for the board exam from NCERT Class 12 Physics chapter 13. Learning the class 12 physics chapter nuclei ncert solutions is important to score well in the board exam. The questions in NCERT Solutions for Class 12 Physics Chapter 13 Nuclei are divided into two parts namely exercise and additional exercise. Nuclei Class 12 NCERT solutions download PDF option is available to read the solution offline.

    Free download physics chapter 13 class 12 ncert solutions pdf for CBSE exam.

    NCERT Solutions for Class 12 Physics Chapter 13 Nuclei

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    NCERT solutions for class 12 physics chapter 13 nuclei: Exercise Solution

    Q.13.1 (a) Two stable isotopes of lithium _{3}^{6}\textrm{Li} and _{3}^{7}\textrm{Li} have respective abundances of 7.5\; ^{o}/_{o} and 92.5\; ^{o}/_{o} . These isotopes have masses 6.01512 \; u and 7.01600 \; u , respectively. Find the atomic mass of lithium.

    Answer:

    Mass of the two stable isotopes and their respective abundances are 6.01512 \; u and 7.01600 \; u and 7.5\; ^{o}/_{o} and 92.5\; ^{o}/_{o} .

    m=\frac{6.01512\times7.5+7.01600\times92.5}{100}

    m=6.940934 u

    Q. 13.1(b) Boron has two stable isotopes, _{5}^{10}\textrm{B} and _{5}^{11}\textrm{B} . Their respective masses are 10.01294 \; u and 11.00931\; u , and the atomic mass of boron is 10.811 u. Find the abundances of _{5}^{10}\textrm{B} and _{5}^{11}\textrm{B} .

    Answer:

    The atomic mass of boron is 10.811 u

    Mass of the two stable isotopes are 10.01294 \; u and 11.00931\; u respectively

    Let the two isotopes have abundances x% and (100-x)%

    \\10.811=\frac{10.01294\times x+11.00931\times(100-x)}{100} \\x=19.89\\ 100-x=80.11

    Therefore the abundance of _{5}^{10}\textrm{B} is 19.89% and that of _{5}^{11}\textrm{B} is 80.11%

    Q. 13.2 The three stable isotopes of neon: _{10}^{20}\textrm{Ne}, _{10}^{21}\textrm{Ne} and _{10}^{22}\textrm{Ne} have respective abundances of 90.51\; ^{o}/_{o} , 0.27\; ^{o}/_{o} and 9.22\; ^{o}/_{o} . The atomic masses of the three isotopes are 19.99\; u, 20.99\; u \; \; and\; \; 21.99 \; u, respectively. Obtain the average atomic mass of neon.

    Answer:

    The atomic masses of the three isotopes are 19.99 u(m 1 ), 20.99 u(m 2 ) and 21.99u(m 3 )

    Their respective abundances are 90.51%(p 1 ), 0.27%(p 2 ) and 9.22%(p 3 )

    \\m= \frac{19.99\times 90.51+20.99\times 0.27+21.99\times 9.22}{100}\\m=20.1771u

    The average atomic mass of neon is 20.1771 u.

    Q. 13.3 Obtain the binding energy( in MeV ) of a nitrogen nucleus (_{7}^{14}\textrm{N}) , given m (_{7}^{14}\textrm{N})=14.00307\; \; u

    Answer:

    m n = 1.00866 u

    m p = 1.00727 u

    Atomic mass of Nitrogen m= 14.00307 u

    Mass defect \Delta m=7 \times m n +7 \times m p - m

    \Delta m=7 \times 1.00866+7 \times 1.00727 - 14.00307

    \Delta m=0.10844

    Now 1u is equivalent to 931.5 MeV

    E b =0.10844 \times 931.5

    E b =101.01186 MeV

    Therefore binding energy of a Nitrogen nucleus is 101.01186 MeV.

    Q. 13.4 (i) Obtain the binding energy of the nuclei _{26}^{56}\textrm{Fe} and _{83}^{209}\textrm{Bi} in units of MeV from the following data:

    (i)m (_{26}^{56}\textrm{Fe})=55.934939\; \; u

    Answer:

    m H = 1.007825 u

    m n = 1.008665 u

    The atomic mass of _{26}^{56}\textrm{Fe} is m=55.934939 u

    Mass defect

    \Delta m=(56-26)\times m_H+26\times m_p - m

    \Delta m=30\times1.008665+26\times1.007825 - 55.934939

    \Delta m=0.528461

    Now 1u is equivalent to 931.5 MeV

    E b =0.528461 \times 931.5

    E b =492.2614215 MeV

    Therefore the binding energy of a _{26}^{56}\textrm{Fe} nucleus is 492.2614215 MeV.

    Average binding energy

    =\frac{492.26}{56}MeV=8.79 MeV

    Q. 13.4 (ii) Obtain the binding energy of the nuclei _{26}^{56}\textrm{Fe} and _{83}^{209}\textrm{Bi} in units of MeV from the following data:

    (ii)m(_{83}^{209}\textrm{Bi})=208.980388\; \; u

    Answer:

    m H = 1.007825 u

    m n = 1.008665 u

    The atomic mass of _{83}^{209}\textrm{Bi} is m=208.980388 u

    Mass defect

    1646201017040

    \Delta m=126 \times 1.008665+83 \times 1.007825 - 208.980388

    \Delta m=1.760877 u

    Now 1u is equivalent to 931.5 MeV

    E b =1.760877 \times 931.5

    E b =1640.2569255 MeV

    Therefore the binding energy of a _{83}^{209}\textrm{Bi} nucleus is 1640.2569255 MeV.

    Average\ binding\ energy=\frac{1640.25}{208.98}=7.84MeV

    Q.13.5 A given coin has a mass of 3.0\; g . Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of _{29}^{63}\textrm{Cu} atoms (of mass 62.92960\; \; u ).

    Answer:

    Mass of the coin is w = 3g

    Total number of Cu atoms in the coin is n

    \\n=\frac{w\times N_{A}}{Atomic\ Mass}\\ n=\frac{3\times 6.023\times 10^{23}}{62.92960}

    n=2.871 \times 10 22

    m H = 1.007825 u

    m n = 1.008665 u

    Atomic mass of _{29}^{63}\textrm{Cu} is m=62.92960 u

    Mass defect \Delta m=(63-29) \times m n +29 \times m H - m

    \Delta m=34 \times 1.008665+29 \times 1.007825 - 62.92960

    \Delta m=0.591935 u

    Now 1u is equivalent to 931.5 MeV

    E b =0.591935 \times 931.5

    E b =551.38745 MeV

    Therefore binding energy of a _{29}^{63}\textrm{Cu} nucleus is 551.38745 MeV.

    The nuclear energy that would be required to separate all the neutrons and protons from each other is

    n \times E b =2.871 \times 10 22 \times 551.38745

    =1.5832 \times 10 25 MeV

    =1.5832 \times 10 25 \times 1.6 \times 10 -19 \times 10 6 J

    =2.5331 \times 10 9 kJ

    Q.13.6 (i) Write nuclear reaction equations for

    (i)\; \alpha -decay\; of\; _{88}^{226}\textrm{Ra}

    Answer:

    The nuclear reaction equations for the given alpha decay

    _{88}^{226}\textrm{Ra}\rightarrow _{86}^{222}\textrm{Rn}+_{2}^{4}\textrm{He}

    Q.13.6 (ii) Write nuclear reaction equations for

    (ii)\; \alpha -decay\; of\; _{94}^{242}\textrm{Pu}

    Answer:

    The nuclear reaction equations for the given alpha decay is

    _{94}^{242}\textrm{Pu}\rightarrow _{92}^{238}\textrm{U}+_{2}^{4}\textrm{He}

    Q.13.6 (iii) Write nuclear reaction equations for

    (iii)\; \beta ^{-} -\: decay\; of\; _{15}^{32}\textrm{P}

    Answer:

    The nuclear reaction equations for the given beta minus decay is

    _{15}^{32}\textrm{P}\rightarrow _{16}^{32}\textrm{S}+e^{-}+\bar{\nu }

    Q.13.6 (iv) Write nuclear reaction equations for

    (iv)\; \beta ^{-} -\: decay\; of\; _{83}^{210}\textrm{Bi}

    Answer:

    The nuclear reaction equation for the given beta minus decay is

    _{83}^{210}\textrm{Bi}\rightarrow _{84}^{210}\textrm{Po}+e^{-}+\bar{\nu }

    Q.13.6 (v) Write nuclear reaction equations for

    (v)\; \beta ^{+} -\: decay\; of\; _{6}^{11}\textrm{C}

    Answer:

    The nuclear reaction for the given beta plus decay will be

    _{6}^{11}\textrm{C}\rightarrow _{5}^{11}\textrm{P}+e^{+}+\nu

    Q.13.6 (vi) Write nuclear reaction equations for

    (vi)\; \beta ^{+} -\: decay\; of\; _{43}^{97}\textrm{Tc}

    Answer:

    nuclear reaction equations for

    \beta ^{+} -\: decay\; of\; _{43}^{97}\textrm{Tc}\ is

    _{43}^{97}\textrm{Tc}\rightarrow _{42}^{97}\textrm{Mo}+e^{+}+\nu

    Q.13.6 (vii) Write nuclear reaction equations for

    Electron capture of _{54}^{120}\textrm{Xe}

    Answer:

    The nuclear reaction for electron capture of _{54}^{120}\textrm{Xe} is

    _{54}^{120}\textrm{Xe}+e^{-}\rightarrow _{53}^{120}\textrm{I}+\nu

    Q. 13.7 A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

    Answer:

    (a) The activity is proportional to the number of radioactive isotopes present

    The number of half years in which the number of radioactive isotopes reduces to x% of its original value is n.

    n=log_{2}(\frac{100}{x})

    In this case

    n=log_{2}(\frac{100}{3.125})=log_{2}32=5

    It will take 5T years to reach 3.125% of the original activity.

    (b) In this case

    n=log_{2}(\frac{100}{1})=log_{2}100=6.64

    It will take 6.64T years to reach 1% of the original activity.

    Q.13.9 Obtain the amount of _{27}^{60}\textrm{Co} necessary to provide a radioactive source of 8.0 mCi strength. The half-life of _{27}^{60}\textrm{Co} is 5.3 years.

    Answer:

    Required activity=8.0 mCi

    1 Ci=3.7 \times 10 10 decay s -1

    8.0 mCi=8 \times 10 -3 \times 3.7 \times 10 10 =2.96 \times 10 8 decay s -1

    T 1/2 =5.3 years

    \lambda =\frac{0.693}{T_{1/2}}

    \lambda =\frac{0.693}{5.3\times 365\times 24\times 3600}

    \lambda =4.14\times 10^{-9}\ s^{-1}

    \\\frac{\mathrm{d} N}{\mathrm{d} t}=-N\lambda \\ N=-\frac{\mathrm{d} N}{\mathrm{d} t}\times \frac{1}{\lambda }\\ N=-(-2.96\times 10^{8})\times \frac{1}{4.14\times 10^{-9}}\\ N=7.15\times 10^{16}\ atoms

    Mass of those many atoms of Cu will be

    w=\frac{7.15\times 10^{16}\times 60}{6.023\times 10^{23}}

    w=7.12\times10^{-6} g

    7.12 \times 10 -6 g of _{27}^{60}\textrm{Co} is necessary to provide a radioactive source of 8.0 mCi strength.

    Q. 13.10 The half-life of _{38}^{90}\textrm{Sr} is 28 years. What is the disintegration rate of 15 mg of this isotope?

    Answer:

    T 1/2 =28 years

    \\\lambda =\frac{0.693}{28\times 365\times 24\times 3600}\\ \lambda =7.85\times 10^{-10} \ decay\ s^{-1}

    The number of atoms in 15 mg of _{38}^{90}\textrm{Sr} is

    N=\frac{15\times 10^{-3}\times 6.023\times 10^{23}}{90}

    N=1.0038 \times 10 20

    The disintegration rate will be

    \frac{\mathrm{d} N}{\mathrm{d} t}=-N\lambda

    =-1.0038 \times 10 20 \times 7.85 \times 10 -10

    =-7.88 \times 10 10 s -1

    The disintegration rate is therefore 7.88 \times 10 10 decay s -1 .

    Q.13.11 Obtain approximately the ratio of the nuclear radii of the gold isotope _{79}^{197}\textrm{Au} and the silver isotope _{47}^{107}\textrm{Ag}

    Answer:

    The nuclear radii are directly proportional to the cube root of the mass number.

    The ratio of the radii of the given isotopes is therefore

    \left ( \frac{197}{107} \right )^{1/3}=1.23

    Q.13.12 Find the Q-value and the kinetic energy of the emitted \alpha -particle in the \alpha -decay of

    (a)\; _{88}^{226}\textrm{Ra}

    Given m(_{88}^{226}\textrm{Ra})=226.02540\; u, m(_{86}^{222}\textrm{Rn})=222.01750\; u,

    m(_{86}^{222}\textrm{Rn})=220.01137\; u, m(_{84}^{216}\textrm{Po})=216.00189\; u,

    Answer:

    Mass defect is \Delta m

    \Delta m=m(_{88}^{226}\textrm{Ra})-m(_{86}^{222}\textrm{Rn})-m(_{2}^{4}\textrm{He})

    \Delta m=226.02540-222.0175-4.002603

    \Delta m=0.005297 u

    1 u = 931.5 MeV/c 2

    Q-value= \Delta m \times 931.5

    =4.934515 MeV

    By using Linear Momentum Conservation and Energy Conservation

    The kinetic energy of alpha particle =

    \frac{mass\ of\ nucleus\ after\ decay}{mass\ of\ nucleus\ before\ decay}\times Q-value

    = \frac{222.01750}{226.0254}\times 4.934515

    =4.847 MeV

    Q.13.12 (b) Find the Q-value and the kinetic energy of the emitted \alpha -particle in the \alpha -decay of

    (b)\; _{86}^{220}\textrm{Rn}

    Given m(_{88}^{226}\textrm{Ra})=226.02540\; u, m(_{86}^{222}\textrm{Rn})=222.01750\; u,

    m(_{86}^{222}\textrm{Rn})=220.01137\; u, m(_{84}^{216}\textrm{Po})=216.00189\; u,

    Answer:

    Mass defect is \Delta m

    \Delta m=m(_{86}^{222}\textrm{Rn})-m(_{84}^{216}\textrm{Po})-m(_{2}^{4}\textrm{He})

    \Delta m=220.01137-216.00189-4.002603

    \Delta m=0.006877 u

    1 u = 931.5 MeV/c 2

    Q-value= \Delta m \times 931.5

    =6.406 MeV

    By using Linear Momentum Conservation and Energy Conservation

    The kinetic energy of alpha particle =

    \frac{mass\ of\ nucleus\ after\ decay}{mass\ of\ nucleus\ before\ decay}\times Q-value

    = \frac{216.00189}{220.01138}\times 6.406

    =6.289 MeV

    Q.13.13 The radionuclide ^{11}C decays according to

    _{6}^{11}\textrm{C}\rightarrow B+e^{+}+v:T_{1/2}=20.3\; min
    The maximum energy of the emitted positron is 0.960\; MeV. .

    Given the mass values:

    m(_{6}^{11}\textrm{C})=11.011434\; u and m(_{6}^{11}\textrm{B})=11.009305\; u
    calculate Q and compare it with the maximum energy of the positron emitted.

    Answer:

    If we use atomic masses

    \\\Delta m=m(_{6}^{11}\textrm{C})-m(_{5}^{11}\textrm{B})-2m_{e}\\ \Delta m=11.011434-11.009305-2\times 0.000548\\ \Delta m=0.001033u

    Q-value= 0.001033 \times 931.5=0.9622 MeV which is comparable with a maximum energy of the emitted positron.

    Q.13.14 The nucleus _{10}^{23}\textrm{Ne} decays by \beta ^{-} emission. Write down the \beta -decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

    (i) m (_{10}^{23}\textrm{Ne} ) = 22.994466 \; u

    (ii) m (_{11}^{23}\textrm{Na} ) = 22.089770 \; u

    Answer:

    The \beta decay equation is

    _{10}^{23}\textrm{Ne}\rightarrow _{11}^{23}\textrm{Na}+e^{-}+\bar{\nu }+Q

    \\\Delta m=m(_{10}^{23}\textrm{Ne})-_{11}^{23}\textrm{Na}-m_{e}\\ \Delta m=22.994466-22.989770\\ \Delta m=0.004696u

    (we did not subtract the mass of the electron as it is cancelled because of the presence of one more electron in the sodium atom)

    Q=0.004696 \times 931.5

    Q=4.3743 eV

    The emitted nucleus is way heavier than the \beta particle and the energy of the antineutrino is also negligible and therefore the maximum energy of the emitted electron is equal to the Q value.

    Q. 13.15 (i) The Q value of a nuclear reaction A + b \rightarrow C + d is defined by Q=[m_{A}+m_{b}-m_{c}-m_{d}]c^{2} where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

    (i) _{1}^{1}\textrm{H}+_{1}^{3}\textrm{H}\rightarrow _{1}^{2}\textrm{H}+_{1}^{2}\textrm{H} the following

    Atomic masses are given to be

    m(_{1}^{2}\textrm{H})=2.014102\; u

    m(_{1}^{3}\textrm{H})=3.0016049\; u

    m(_{6}^{12}\textrm{H})=12.000000\; u

    m(_{10}^{20}\textrm{Ne})=19.992439\; u

    Answer:

    \\\Delta m=m(_{1}^{1}\textrm{H})+m(_{1}^{3}\textrm{H})-2m(_{1}^{2}\textrm{H})\\ \Delta m=1.007825+3.0016049-2\times 2.014102\\ \Delta m=-0.00433

    The above negative value of mass defect implies there will be a negative Q value and therefore the reaction is endothermic

    Q. 13.15 (ii) The Q value of a nuclear reaction A + b \rightarrow C + d is defined by Q=[m_{A}+m_{b}-m_{c}-m_{d}]c^{2} where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

    (ii) _{6}^{12}\textrm{C}+_{6}^{12}\textrm{C}\rightarrow _{10}^{20}\textrm{Ne}+_{2}^{4}\textrm{He}

    Atomic masses are given to be

    m(_{1}^{2}\textrm{H})=2.014102\; u

    m(_{1}^{3}\textrm{H})=3.0016049\; u

    m(_{6}^{12}\textrm{H})=12.000000\; u

    m(_{10}^{20}\textrm{Ne})=19.992439\; u

    Answer:

    \\\Delta m=2m(_{6}^{12}\textrm{C})-m(_{10}^{20}\textrm{Ne})-m(_{2}^{4}\textrm{He})\\ \Delta m=2\times 12.00000-19.992439-4.002603\\ \Delta m=0.004958

    The above positive value of mass defect implies Q value would be positive and therefore the reaction is exothermic

    Q.13.16 Suppose, we think of fission of a _{26}^{56}\textrm{Fe} nucleus into two equal fragments, _{13}^{28}\textrm{Al} . Is the fission energetically possible? Argue by working out Q of the process. Given m ( _{26}^{56}\textrm{Fe} ) = 55.93494\; u and m ( _{13}^{28}\textrm{Al} ) = 27.98191\; u

    Answer:

    The reaction will be _{26}^{56}\textrm{Fe}\rightarrow _{13}^{28}\textrm{Al}+_{13}^{28}\textrm{Al}

    The mass defect of the reaction will be

    \\\Delta m=m(_{26}^{56}\textrm{Fe})-2m( _{13}^{28}\textrm{Al})\\ \Delta m=55.93494-2\times 27.98191\\ \Delta m=-0.02888u

    Since the mass defect is negative the Q value will also negative and therefore the fission is not energetically possible

    Q. 13.17 The fission properties of _{94}^{239}\textrm{Pu} are very similar to those of _{92}^{235}\textrm{U} . The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure _{94}^{239}\textrm{Pu} undergo fission?

    Answer:

    Number of atoms present in 1 kg(w) of _{94}^{239}\textrm{Pu} =n

    \\n=\frac{w\times N_{A}}{mass\ number\ of\ Pu}\\ n=\frac{1000\times 6.023\times 10^{23}}{239}\\n=2.52\times 10^{24}

    Energy per fission (E)=180 MeV

    Total Energy released if all the atoms in 1 kg _{94}^{239}\textrm{Pu} undergo fission = E \times n

    =180 \times 2.52 \times 10 24

    =4.536 \times 10 26 MeV

    Q. 13.18 A 1000\; MW fission reactor consumes half of its fuel in 5.00 \; y . How much _{92}^{235}\textrm{U} did it contain initially? Assume that the reactor operates 80\; ^{}o/_{0} of the time, that all the energy generated arises from the fission of _{92}^{235}\textrm{U} and that this nuclide is consumed only by the fission process.

    Answer:

    The amount of energy liberated on fission of 1 _{92}^{235}\textrm{U} atom is 200 MeV.

    The amount of energy liberated on fission of 1g _{92}^{235}\textrm{U}

    \\=\frac{200\times 10^{6} \times 1.6\times 10^{-19}\times 6.023\times 10^{23}}{235}\\=8.2\times 10^{10}\ Jg^{-1}

    Total Energy produced in the reactor in 5 years

    \\=1000\times 10^{6}\times 0.8\times 5\times 365\times 24\times 3600\\ =1.261\times 10^{17}\ J

    Mass of _{92}^{235}\textrm{U} which underwent fission, m

    =\frac{1.261\times 10^{17}}{8.2\times 10^{10}}

    =1537.8 kg

    The amount present initially in the reactor = 2m

    =2 \times 1537.8

    =3075.6 kg

    Q. 13.19 How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as

    _{1}^{2}\textrm{H}+_{1}^{2}\textrm{H}\rightarrow _{2}^{3}\textrm{He}+n+3.27\; MeV

    Answer:

    The energy liberated on the fusion of two atoms of deuterium= 3.27 MeV

    Number of fusion reactions in 2 kg of deuterium = N A \times 500

    The energy liberated by fusion of 2.0 kg of deuterium atoms E

    \\=3.27\times 10^{6}\times 1.6\times 10^{-19}\times 6.023\times 10^{23}\times 500\\=1.576\times 10^{14}\ J

    Power of lamp (P)= 100 W

    Time the lamp would glow using E amount of energy is T=

    \\=\frac{E}{P}\\ =\frac{1.576\times 10^{14}}{100\times 3600\times 24\times 365}

    =4.99 \times 10 4 years

    Q. 13.20 Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)

    Answer:

    For a head-on collision of two deuterons, the closest distances between their centres will be d=2 \times r

    d=2 \times 2.0

    d=4.0 fm

    d=4 \times 10 -15 m

    charge on each deuteron = charge of one proton=q =1.6 \times 10 -19 C

    The maximum electrostatic potential energy of the system during the head-on collision will be E

    \\=\frac{q^{2}}{4\pi \epsilon _{0}d}\\ =\frac{9\times 10^{9}\times (1.6\times 10^{-19})^{2}}{4\times 10^{-15}}\ J\\ =\frac{9\times 10^{9}\times (1.6\times 10^{-19})^{2}}{4\times 10^{-15}\times 1.6\times 10^{-19}}\ eV\\=360\ keV

    The above basically means to bring two deuterons from infinity to each other would require 360 keV of work to be done or would require 360 keV of energy to be spent.

    Q. 13.21 From the relation R=R_{0}A^{1/3} , where R_{0} is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

    Answer:

    Mass of an element with mass number A will be about A u. The density of its nucleus, therefore, would be

    \\d=\frac{m}{v}\\ d=\frac{A}{\frac{4\pi }{3}R^{3}}\\d=\frac{A}{\frac{4\pi }{3}(R_{0}A^{1/3})^{3}}\\d=\frac{3}{4\pi R{_{0}}^{3}}

    As we can see the above density comes out to be independent of mass number A and R 0 is constant, so matter density is nearly constant

    Q. 13.22 For the \beta ^{+} (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K–shell, is captured by the nucleus and a neutrino is emitted).

    e^{+}+_{z}^{A}\textrm{X}\rightarrow _{Z-1}^{A}\textrm{Y}+v

    Show that if \beta ^{+} emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.

    Answer:

    For the electron capture, the reaction would be

    _{Z}^{A}\textrm{X}+e^{-}\rightarrow _{Z-1}^{A}\textrm{Y}+\nu +Q_{1}

    The mass defect and q value of the above reaction would be

    \\\Delta m_{1}=m(_{Z}^{A}\textrm{X})+m_{e}-m(_{Z-1}^{A}\textrm{Y})\\ Q_{1}=([m(_{Z}^{A}\textrm{X})-m(_{Z-1}^{A}\textrm{Y})]+m_{e})c^{2}

    where m N (_{Z}^{A}\textrm{X}) and m N (_{Z-1}^{A}\textrm{Y}) are the nuclear masses of elements X and Y respectively

    For positron emission, the reaction would be

    _{Z}^{A}\textrm{X}\rightarrow _{Z-1}^{A}\textrm{Y}+e^{+}+\bar{\nu }+Q_{2}

    The mass defect and q value for the above reaction would be

    \\\Delta m_{2}=m(_{Z}^{A}\textrm{X})-m(_{Z-1}^{A}\textrm{Y})-m_{e}\\ Q_{2}=([m(_{Z}^{A}\textrm{X})-m(_{Z-1}^{A}\textrm{Y})]-m_{e})c^{2}

    From the above values, we can see that if Q 2 is positive Q 1 will also be positive but Q 1 being positive does not imply that Q 2 will also have to positive.


    NCERT solutions for class 12 physics chapter 13 nuclei: Additional Exercise Solution

    Q.13.23 In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are _{12}^{24}\textrm{Mg}(23.98504\; u) , _{12}^{25}\textrm{Mg}(24.98584\; u) and _{12}^{26}\textrm{Mg}(25.98259\; u) . The natural abundance of is 78.99% by mass. Calculate the abundances of other two isotopes.

    Answer:

    Let the abundances of _{12}^{25}\textrm{Mg} and _{12}^{26}\textrm{Mg} be x and y respectively.

    x+y+78.99=100

    y=21.01-x

    The average atomic mass of Mg is 24.312 u

    \\24.312=\frac{78.99\times 23.98504+x\times 24.98584+(100-x)\times 25.98259}{100}\\ x\approx 9.3\\ y=21.01-x\\ y=21.01-9.3\\ y=11.71

    The abundances of _{12}^{25}\textrm{Mg} and _{12}^{26}\textrm{Mg} are 9.3% and 11.71% respectively

    Q.13.24 (i) The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei _{20}^{41}\textrm{Ca} from the following data:

    m(_{20}^{40}\textrm{Ca})=39.962591\; u

    m(_{20}^{41}\textrm{Ca})=40.962278 \; u

    m(_{13}^{26}\textrm{Al})=25.986895 \; u

    m(_{13}^{27}\textrm{Al})=26.981541 \; u

    Answer:

    The reaction showing the neutron separation is

    _{20}^{41}\textrm{Ca}+E\rightarrow _{20}^{40}\textrm{Ca}+_{0}^{1}\textrm{n}

    \\E=(m(_{20}^{40}\textrm{Ca})+m(_{0}^{1}\textrm{n})-m(_{20}^{41}\textrm{Ca}))c^{2}\\ E=(39.962591+1.008665-40.962278)c^{2}\\ E=(0.008978)u\times c^{2}

    But 1u=931.5 MeV/c 2

    Therefore E=(0.008978) \times 931.5

    E=8.363007 MeV

    Therefore to remove a neutron from the _{20}^{41}\textrm{Ca} nucleus 8.363007 MeV of energy is required

    Q.13.24 (ii) The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei _{13}^{27}\textrm{Al} from the following data:

    m(_{20}^{40}\textrm{Ca})=39.962591\; u

    m(_{20}^{41}\textrm{Ca})=40.962278 \; u

    m(_{13}^{26}\textrm{Al})=25.986895 \; u

    m(_{13}^{27}\textrm{Al})=26.981541 \; u

    Answer:

    The reaction showing the neutron separation is

    _{13}^{27}\textrm{Al}+E\rightarrow _{13}^{26}\textrm{Al}+_{0}^{1}\textrm{n}

    \\E=(m(_{13}^{26}\textrm{Ca})+m(_{0}^{1}\textrm{n})-m(_{13}^{27}\textrm{Ca}))c^{2}\\ E=(25.986895+1.008665-26.981541)c^{2}\\ E=(0.014019)u\times c^{2}

    But 1u=931.5 MeV/c 2

    Therefore E=(0.014019) \times 931.5

    E=13.059 MeV

    Therefore to remove a neutron from the _{13}^{27}\textrm{Al} nucleus 13.059 MeV of energy is required

    Q.13.25 A source contains two phosphorous radio nuclides _{15}^{32}\textrm{P}(T_{1/2}=14.3d) and _{15}^{33}\textrm{P}(T_{1/2}=25.3d) . Initially, 10% of the decays come from _{15}^{33}\textrm{P} . How long one must wait until 90% do so?

    Answer:

    Let initially there be N 1 atoms of _{15}^{32}\textrm{P} and N 2 atoms of _{15}^{33}\textrm{P} and let their decay constants be \lambda _{1} and \lambda _{2} respectively

    Since initially the activity of _{15}^{33}\textrm{P} is 1/9 times that of _{15}^{32}\textrm{P} we have

    N_{1 } \lambda_{1}=\frac{N_{2}\lambda _{2}}{9} (i)

    Let after time t the activity of _{15}^{33}\textrm{P} be 9 times that of _{15}^{32}\textrm{P}

    N_{1 } \lambda_{1}e^{-\lambda _{1}t}=9N_{2}\lambda _{2}e^{-\lambda _{2}t} (ii)

    Dividing equation (ii) by (i) and taking the natural log of both sides we get

    \\-\lambda _{1}t=ln81-\lambda _{2}t \\t=\frac{ln81}{\lambda _{2}-\lambda _{1}}

    where \lambda _{2}=0.048/ day and \lambda _{1}=0.027/ day

    t comes out to be 208.5 days

    Q.13.26 Under certain circumstances, a nucleus can decay by emitting a particle more massive than an \alpha -particle. Consider the following decay processes:

    _{88}^{223}\textrm{Ra}\rightarrow _{82}^{209}\textrm{Pb}+_{6}^{14}\textrm{C}

    _{88}^{223}\textrm{Ra}\rightarrow _{86}^{219}\textrm{Rn}+_{2}^{4}\textrm{He}

    Calculate the Q-values for these decays and determine that both are energetically allowed.

    Answer:

    _{88}^{223}\textrm{Ra}\rightarrow _{82}^{209}\textrm{Pb}+_{6}^{14}\textrm{C}

    \\\Delta m=m(_{88}^{223}\textrm{Ra})-m(_{82}^{209}\textrm{Pb})-m(_{6}^{14}\textrm{C})\\ =223.01850-208.98107-14.00324 \\=0.03419u

    1 u = 931.5 MeV/c 2

    Q=0.03419 \times 931.5

    =31.848 MeV

    As the Q value is positive the reaction is energetically allowed

    _{88}^{223}\textrm{Ra}\rightarrow _{86}^{219}\textrm{Rn}+_{2}^{4}\textrm{He}

    \\\Delta m=m(_{88}^{223}\textrm{Ra})-m(_{86}^{219}\textrm{Rn})-m(_{2}^{4}\textrm{He})\\ =223.01850-219.00948-4.00260 \\=0.00642u

    1 u = 931.5 MeV/c 2

    Q=0.00642 \times 931.5

    =5.98 MeV

    As the Q value is positive the reaction is energetically allowed

    Q.13.27 Consider the fission of _{92}^{238}\textrm{U} by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are _{58}^{140}\textrm{Ce} and _{44}^{99}\textrm{Ru} . Calculate Q for this fission process. The relevant atomic and particle masses are

    m(_{92}^{238}\textrm{U})=238.05079\; u

    m(_{58}^{140}\textrm{Ce})=139.90543\; u

    m(_{44}^{99}\textrm{Ru})= 98.90594\; u

    Answer:

    The fission reaction given in the question can be written as

    _{92}^{238}\textrm{U}+_{0}^{1}\textrm{n}\rightarrow _{58}^{140}\textrm{Ce}+_{44}^{99}\textrm{Ru}+10e^{-}

    The mass defect for the above reaction would be

    \Delta m=m_{N}(_{92}^{238}\textrm{U})+m(_{0}^{1}\textrm{n})-m_{N}(_{58}^{140}\textrm{Ce})-m_{N}(_{44}^{99}\textrm{Ce})-10m_{e}

    In the above equation, m N represents nuclear masses

    \\\Delta m=m(_{92}^{238}\textrm{U})-92m_{e}+m(_{0}^{1}\textrm{n})-m(_{58}^{140}\textrm{Ce})+58m_{e}-m(_{44}^{99}\textrm{Ru})+44m_{e}-10m_{e} \\\Delta m=m(_{92}^{238}\textrm{U})+m(_{0}^{1}\textrm{n})-m(_{58}^{140}\textrm{Ce})-m(_{44}^{99}\textrm{Ru})\\ \Delta m=238.05079+1.008665-139.90543-98.90594\\ \Delta m=0.247995u

    but 1u =931.5 MeV/c 2

    Q=0.247995 \times 931.5

    Q=231.007 MeV

    Q value of the fission process is 231.007 MeV

    Q.13.28 (i) Consider the D–T reaction (deuterium-tritium fusion)

    _{1}^{2}\textrm{H}+_{1}^{3}\textrm{H}\rightarrow _{2}^{4}\textrm{He}+n

    (a) Calculate the energy released in MeV in this reaction from the data:

    m(_{1}^{2}\textrm{H})=2.014102\; u

    m(_{1}^{3}\textrm{H})=3.016049\; u

    Answer:

    The mass defect of the reaction is

    \\\Delta m=m(_{1}^{2}\textrm{H})+m(_{1}^{3}\textrm{H})-m(_{2}^{4}\textrm{He})-m(_{0}^{1}\textrm{n})\\ \Delta m=2.014102+3.016049-4.002603-1.008665\\ \Delta m=0.018883u

    1u = 931.5 MeV/c 2

    Q=0.018883 \times 931.5=17.59 MeV

    Q.13.28 (b) Consider the D–T reaction (deuterium–tritium fusion)

    _{1}^{2}\textrm{H}+_{1}^{3}\textrm{H}\rightarrow _{2}^{4}\textrm{He}+n

    (b) Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion event =average thermal kinetic energy available with the interacting particles = 2(3kT/2) ; k = Boltzman’s constant, T = absolute temperature.)

    Answer:

    To initiate the reaction both the nuclei would have to come in contact with each other.

    Just before the reaction the distance between their centres would be 4.0 fm.

    The electrostatic potential energy of the system at that point would be

    \\U=\frac{q^{2}}{4\pi \epsilon _{0}d}\\ U=\frac{9\times 10^{9}(1.6\times 10^{-19})^{2}}{4\times 10^{-15}}\\U=5.76\times 10^{-14}J

    The same amount of Kinetic Energy K would be required to overcome the electrostatic forces of repulsion to initiate the reaction

    It is given that K=2\times \frac{3kT}{2}

    Therefore the temperature required to initiate the reaction is

    \\T=\frac{K}{3k}\\ =\frac{5.76\times 10^{-14}}{3\times 1.38\times 10^{-23}}\\=1.39\times 10^{9}\ K

    Q. 13.29 Obtain the maximum kinetic energy of \beta - particles, and the radiation frequencies of \gamma decays in the decay scheme shown in Fig. 13.6. You are given that

    m(^{198}Au)=197.968233\; u

    m(^{198}Hg)=197.966760 \; u

    1594197218194

    Answer:

    \gamma _{1} decays from 1.088 MeV to 0 V

    Frequency of \gamma _{1} is

    \\\nu _{1}=\frac{1.088\times 10^{6}\times 1.6\times 10^{-19}}{6.62\times 10^{-34}}\\ \nu _{1}=2.637\times 10^{20}\ Hz Plank's constant, h=6.62 \times 10 -34 Js E=h\nu

    Similarly, we can calculate frequencies of \gamma _{2} and \gamma _{3}

    \\\nu _{2}=9.988\times 10^{19}\ Hz\\ \nu _{3}=1.639\times 10^{20}\ Hz

    The energy of the highest level would be equal to the energy released after the decay

    Mass defect is

    \\\Delta m=m(_{79}^{196}\textrm{U})-m(_{80}^{196}\textrm{Hg})\\ \Delta m=197.968233-197.966760\\\Delta m=0.001473u

    We know 1u = 931.5 MeV/c 2

    Q value= 0.001473 \times 931.5=1.3721 MeV

    The maximum Kinetic energy of \beta _{1}^{-} would be 1.3721-1.088=0.2841 MeV

    The maximum Kinetic energy of \beta _{2}^{-} would be 1.3721-0.412=0.9601 MeV

    Q. 13.30 Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of 235U in a fission reactor.

    Answer:

    (a) _{1}^{1}\textrm{H} _{1}^{1}\textrm{H}+_{1}^{1}\textrm{H}+_{1}^{1}\textrm{H}+_{1}^{1}\textrm{H}\rightarrow _{2}^{4}\textrm{He}

    The above fusion reaction releases the energy of 26 MeV

    Number of Hydrogen atoms in 1.0 kg of Hydrogen is 1000N A

    Therefore 250N A such reactions would take place

    The energy released in the whole process is E 1

    \\=250\times 6.023\times 10^{23}\times 26\times 10^{6}\times 1.6\times 10^{-19}\\=6.2639\times 10^{14}\ J

    (b) The energy released in fission of one _{92}^{235}\textrm{U} atom is 200 MeV

    Number of _{92}^{235}\textrm{U} atoms present in 1 kg of _{92}^{235}\textrm{U} is N

    \\N=\frac{1000\times 6.023\times 10^{23}}{235}\\ N=2.562\times 10^{24}

    The energy released on fission of N atoms is E 2

    \\E=2.562\times 10^{24}\times 200\times 10^{6}\times 1.6\times 10^{-19}\\ E=8.198\times 10^{13}J

    \frac{E_{1}}{E_{2}}=\frac{6.2639\times 10^{14}}{8.198\times 10^{13}}\approx 8

    Q. 13.31 Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of 235U to be about 200MeV.

    Answer:

    Let the amount of energy to be produced using nuclear power per year in 2020 is E

    E=\frac{200000\times 10^{6}\times 0.1\times 365\times 24\times 3600}{0.25}\ J

    (Only 10% of the required electrical energy is to be produced by Nuclear power and only 25% of therm-nuclear is successfully converted into electrical energy)

    Amount of Uranium required to produce this much energy is M

    =\frac{200000\times 10^{6}\times 0.1\times 365\times 24\times 3600\times 235}{0.25\times 200\times 10^{6}\times 1.6\times 10^{-19}\times 6.023\times 10^{23}\times 1000} (N A =6.023 \times 10 23 , Atomic mass of Uranium is 235 g)

    =3.076 \times 10 4 kg

    This chapter revolves around the topic of 'Nuclei,' and class 12 physics chapter 13 exercise solutions are vital for several reasons. Firstly, understanding nuclear physics is crucial as it forms the basis for numerous advanced concepts. Secondly, scoring in this chapter can be relatively easier compared to some other physics chapters, provided one grasps the fundamentals. The exercise solutions provide a comprehensive breakdown of each question, aiding students in mastering this essential topic effectively and efficiently, even within a limited time frame.

    NCERT solutions for class 12 physics chapter-wise

    Class 12 Physics Chapter Nuclei NCERT Solutions: Important Formulas and Diagrams

    The following formulas will be helpful to understand the NCERT solutions for Class 12 Physics chapter 13 Nuclei

    • Radii of the nuclei, R=R_0A^{\frac{1}{3}}

    Where A is the mass number and R_0=1.2fm

    • Mass defect: \Delta M=(Zm_p+(A-Z)m_n)-M

    Here Z is the atomic number, M is the mass of the nucleus and A is the mass number. This equation tells that the mass of the nucleus is always less than the mass of their constituents.

    E_b=\Delta Mc^2

    Where c is the speed of light.

    • Another main concept of NCERT is the law of radioactive decay. This is given by N=N_0e^{-\lambda t}

    Where N is the number of nuclei at any time t, N_0 is the number of nuclei at any time t_0 and lambda is disintegration constant.

    • The half-life of a radionuclide is given by T_{\frac{1}{2}}=\frac{ln2}{\lambda}

    Where lambda is the disintegration constant.

    After completing all these topics try to do NCERT class 12 chapter 13 exercises. If you are unable to solve or have any doubts refer to the solutions of NCERT class 12 physics chapter 13 nuclei provided below.

    Significance of NCERT solutions for class 12 physics chapter 13 nuclei:

    • About 6% of questions are expected from the chapters atoms and NCERT Class 12th Physics Nuclei for CBSE board exams.
    • The NCERT Class 12 Physics solutions chapter 13 will help to score well in this chapter.
    • The topic of radioactive decay and half-life is important for the board and competitive exams like NEET and JEE Main.
    • Sometimes same questions which are discussed in the solutions of NCERT class 12 Physics chapter 13 solutions come in the CBSE12th exam.

    Key Features of Physics Chapter 13 Class 12 NCERT Solutions

    1. Comprehensive Coverage: These class 12 nuclei ncert solutions encompass all topics and questions found in Chapter 13, ensuring a thorough understanding of nuclear physics.

    2. Detailed Explanations: Each nuclei class 12 ncert solutions offers comprehensive, step-by-step explanations, making complex nuclear physics concepts accessible to students.

    3. Clarity and Simplicity: The class 12 physics chapter nuclei ncert solutions are presented in clear and straightforward language, ensuring ease of understanding.

    4. Practice Questions: Exercise questions are included for practice and self-assessment, enhancing students' problem-solving skills.

    5. Exam Preparation: These physics chapter 13 class 12 ncert solutions are essential for board exam preparation and provide valuable support for competitive exams.

    6. Foundation for Advanced Study: The concepts explored in this chapter serve as the foundation for more advanced studies in nuclear physics and related fields.

    7. Free Access: These solutions are available for free, ensuring accessibility to all students

    NCERT solutions subject wise

    NCERT Exemplar Class 12 Solutions

    Also Check NCERT Books and NCERT Syllabus here:

    Frequently Asked Question (FAQs)

    1. What is the weightage of the chapter nuclei for CBSE board exam

    For CBSE board exam from NCERT class, 12 chapters 13 around 4 to 6 marks questions can be expected. All topics of the NCERT syllabus for the chapter Nuclei should be covered for the CBSE board exam.

    2. Is the chapter Nuclei important for NEET and JEE Main

    Yes the NCERT chapter Nuclei are important for both the exams. Both in NEET and JEE main syllabus the chapter Nuclei is present and 1 or 2 questions from the chapter can be expected for the exams. The questions discussed in the NCERT Solutions for the chapter Nuclei will give a better idea on how to use the formulas and give a better understanding of the concepts discussed.

    3. What is the composition of the nucleus according to nuclei ncert solutions?

    The nucleus is made up of protons, which are positively charged particles, and neutrons, which are neutral particles.

    4. According to nuclei class 12 what is isotopes?

    Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons in their nuclei.

    5. How nuclei class 12 ncert solutions is important for Board?

    nuclei ncert solutions are important for the Board exam as they provide clear explanations, help in solving questions, cover all important topics, provide a structured approach to solving problems, and are designed with the exam pattern in mind, helping in exam-oriented preparation.



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    Questions related to CBSE Class 12th

    Have a question related to CBSE Class 12th ?

    hello,

    Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.

    I hope this was helpful!

    Good Luck

    Hello dear,

    If you was not able to clear 1st compartment and now you giving second compartment so YES, you can go for your improvement exam next year but if a student receives an improvement, they are given the opportunity to retake the boards as a private candidate the following year, but there are some requirements. First, the student must pass all of their subjects; if they received a compartment in any subject, they must then pass the compartment exam before being eligible for the improvement.


    As you can registered yourself as private candidate for giving your improvement exam of 12 standard CBSE(Central Board of Secondary Education).For that you have to wait for a whole year which is bit difficult for you.


    Positive side of waiting for whole year is you have a whole year to preparing yourself for your examination. You have no distraction or something which may causes your failure in the exams. In whole year you have to stay focused on your 12 standard examination for doing well in it. By this you get a highest marks as a comparison of others.


    Believe in Yourself! You can make anything happen


    All the very best.

    Hello Student,

    I appreciate your Interest in education. See the improvement is not restricted to one subject or multiple subjects  and  we cannot say if improvement in one subject in one year leads to improvement in more subjects in coming year.

    You just need to have a revision of all subjects what you have completed in the school. have a revision and practice of subjects and concepts helps you better.

    All the best.

    If you'll do hard work then by hard work of 6 months you can achieve your goal but you have to start studying for it dont waste your time its a very important year so please dont waste it otherwise you'll regret.

    Yes, you can take admission in class 12th privately there are many colleges in which you can give 12th privately.

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    A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

    Option 1)

    0.34\; J

    Option 2)

    0.16\; J

    Option 3)

    1.00\; J

    Option 4)

    0.67\; J

    A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

    Option 1)

    2.45×10−3 kg

    Option 2)

     6.45×10−3 kg

    Option 3)

     9.89×10−3 kg

    Option 4)

    12.89×10−3 kg

     

    An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

    Option 1)

    2,000 \; J - 5,000\; J

    Option 2)

    200 \, \, J - 500 \, \, J

    Option 3)

    2\times 10^{5}J-3\times 10^{5}J

    Option 4)

    20,000 \, \, J - 50,000 \, \, J

    A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

    Option 1)

    K/2\,

    Option 2)

    \; K\;

    Option 3)

    zero\;

    Option 4)

    K/4

    In the reaction,

    2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

    Option 1)

    11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

    Option 2)

    6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

    Option 3)

    33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

    Option 4)

    67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

    How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

    Option 1)

    0.02

    Option 2)

    3.125 × 10-2

    Option 3)

    1.25 × 10-2

    Option 4)

    2.5 × 10-2

    If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

    Option 1)

    decrease twice

    Option 2)

    increase two fold

    Option 3)

    remain unchanged

    Option 4)

    be a function of the molecular mass of the substance.

    With increase of temperature, which of these changes?

    Option 1)

    Molality

    Option 2)

    Weight fraction of solute

    Option 3)

    Fraction of solute present in water

    Option 4)

    Mole fraction.

    Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

    Option 1)

    twice that in 60 g carbon

    Option 2)

    6.023 × 1022

    Option 3)

    half that in 8 g He

    Option 4)

    558.5 × 6.023 × 1023

    A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

    Option 1)

    less than 3

    Option 2)

    more than 3 but less than 6

    Option 3)

    more than 6 but less than 9

    Option 4)

    more than 9

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    Finance Executive

    A career as a Finance Executive requires one to be responsible for monitoring an organisation's income, investments and expenses to create and evaluate financial reports. His or her role involves performing audits, invoices, and budget preparations. He or she manages accounting activities, bank reconciliations, and payable and receivable accounts.  

    3 Jobs Available
    Investment Banker

    An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

    3 Jobs Available
    Bank Branch Manager

    Bank Branch Managers work in a specific section of banking related to the invention and generation of capital for other organisations, governments, and other entities. Bank Branch Managers work for the organisations and underwrite new debts and equity securities for all type of companies, aid in the sale of securities, as well as help to facilitate mergers and acquisitions, reorganisations, and broker trades for both institutions and private investors.

    3 Jobs Available
    Treasurer

    Treasury analyst career path is often regarded as certified treasury specialist in some business situations, is a finance expert who specifically manages a company or organisation's long-term and short-term financial targets. Treasurer synonym could be a financial officer, which is one of the reputed positions in the corporate world. In a large company, the corporate treasury jobs hold power over the financial decision-making of the total investment and development strategy of the organisation.

    3 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    Transportation Planner

    A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

    3 Jobs Available
    Naval Architect

    A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability. 

    2 Jobs Available
    Welding Engineer

    Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

    2 Jobs Available
    Field Surveyor

    Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials. 

    2 Jobs Available
    Highway Engineer

    Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

    2 Jobs Available
    Conservation Architect

    A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

    2 Jobs Available
    Safety Manager

    A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

    2 Jobs Available
    Team Lead

    A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

    2 Jobs Available
    Orthotist and Prosthetist

    Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

    6 Jobs Available
    Veterinary Doctor

    A veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.

    5 Jobs Available
    Pathologist

    A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

    5 Jobs Available
    Gynaecologist

    Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

    4 Jobs Available
    Oncologist

    An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

    3 Jobs Available
    Surgical Technologist

    When it comes to an operation theatre, there are several tasks that are to be carried out before as well as after the operation or surgery has taken place. Such tasks are not possible without surgical tech and surgical tech tools. A single surgeon cannot do it all alone. It’s like for a footballer he needs his team’s support to score a goal the same goes for a surgeon. It is here, when a surgical technologist comes into the picture. It is the job of a surgical technologist to prepare the operation theatre with all the required equipment before the surgery. Not only that, once an operation is done it is the job of the surgical technologist to clean all the equipment. One has to fulfil the minimum requirements of surgical tech qualifications. 

    Also Read: Career as Nurse

    3 Jobs Available
    Maxillofacial Surgeon

    A Maxillofacial Surgeon is a medical professional who performs facial surgeries that include tooth implant, neck, head or other surgeries such as removal of tumours, cosmetic surgeries and treatment of injuries on the face. 

    2 Jobs Available
    Surgical Assistant

    Surgical assistants are professionals in the service of saving others’ lives. They perform various medical procedures. In a career as a surgical assistant, one works in a team and contributes to the success of operations. Surgical assistants learn new procedures and update their knowledge of new medical technology and equipment. Surgical assistants clean and sterilize the tools used in surgery. In a career as a surgical assistant, individuals perform all the basic duties that allow surgeons to keep their focus on essential technical functions.

    2 Jobs Available
    Actor

    For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

    4 Jobs Available
    Acrobat

    Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

    3 Jobs Available
    Video Game Designer

    Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

    3 Jobs Available
    Talent Agent

    The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

    If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

    3 Jobs Available
    Radio Jockey

    Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

    A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

    3 Jobs Available
    Producer

    An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story. 

    They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

    2 Jobs Available
    Fashion Blogger

    Fashion bloggers use multiple social media platforms to recommend or share ideas related to fashion. A fashion blogger is a person who writes about fashion, publishes pictures of outfits, jewellery, accessories. Fashion blogger works as a model, journalist, and a stylist in the fashion industry. In current fashion times, these bloggers have crossed into becoming a star in fashion magazines, commercials, or campaigns. 

    2 Jobs Available
    Photographer

    Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

    2 Jobs Available
    Copy Writer

    In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

    5 Jobs Available
    Journalist

    Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

    3 Jobs Available
    Publisher

    For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

    3 Jobs Available
    Vlogger

    In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

    3 Jobs Available
    Editor

    Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

    3 Jobs Available
    Content Writer

    Content writing is meant to speak directly with a particular audience, such as customers, potential customers, investors, employees, or other stakeholders. The main aim of professional content writers is to speak to their targeted audience and if it is not then it is not doing its job. There are numerous kinds of the content present on the website and each is different based on the service or the product it is used for.

    2 Jobs Available
    Reporter

    Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.  

    2 Jobs Available
    Linguist

    Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning). 

    Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian

    2 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    Quality Controller

    A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

    A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

    3 Jobs Available
    Production Manager

    Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers. 

    Resource Links for Online MBA 

    3 Jobs Available
    Team Lead

    A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

    2 Jobs Available
    Quality Systems Manager

    A Quality Systems Manager is a professional responsible for developing strategies, processes, policies, standards and systems concerning the company as well as operations of its supply chain. It includes auditing to ensure compliance. It could also be carried out by a third party. 

    2 Jobs Available
    Merchandiser

    A career as a merchandiser requires one to promote specific products and services of one or different brands, to increase the in-house sales of the store. Merchandising job focuses on enticing the customers to enter the store and hence increasing their chances of buying a product. Although the buyer is the one who selects the lines, it all depends on the merchandiser on how much money a buyer will spend, how many lines will be purchased, and what will be the quantity of those lines. In a career as merchandiser, one is required to closely work with the display staff in order to decide in what way a product would be displayed so that sales can be maximised. In small brands or local retail stores, a merchandiser is responsible for both merchandising and buying. 

    2 Jobs Available
    Procurement Manager

    The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness. 

    2 Jobs Available
    Production Planner

    Individuals who opt for a career as a production planner are professionals who are responsible for ensuring goods manufactured by the employing company are cost-effective and meets quality specifications including ensuring the availability of ready to distribute stock in a timely fashion manner. 

    2 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    ITSM Manager

    ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks. 

    3 Jobs Available
    Information Security Manager

    Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

    3 Jobs Available
    Computer Programmer

    Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

    3 Jobs Available
    Computer System Analyst

    Individuals in the computer systems analyst career path study the hardware and applications that are part of an organization's computer systems, as well as how they are used. They collaborate closely with managers and end-users to identify system specifications and business priorities, as well as to assess the efficiency of computer systems and create techniques to boost IT efficiency. Individuals who opt for a career as a computer system analyst support the implementation, modification, and debugging of new systems after they have been installed.

    2 Jobs Available
    Test Manager

    A Test Manager is a professional responsible for planning, coordinating and controlling test activities. He or she develops test processes and strategies to analyse and determine test methods and tools for test activities. The test manager jobs involve documenting tests that have been carried out, analysing and evaluating software quality to determine further recommended procedures. 

    2 Jobs Available
    Azure Developer

    A career as Azure Developer comes with the responsibility of designing and developing cloud-based applications and maintaining software components. He or she possesses an in-depth knowledge of cloud computing and Azure app service. 

    2 Jobs Available
    Deep Learning Engineer

    A Deep Learning Engineer is an IT professional who is responsible for developing and managing data pipelines. He or she is knowledgeable about analyzing and storing data collected from various sources.  A Career as a Deep Learning Engineer needs to help the  data scientists and analysts to create effective data sets.

    2 Jobs Available
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