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The Class 12 Physics chapter 13 notes are based on NCERT chapter 13. The NCERT Class 12 Physics chapter 13 notes covers a brief outline of the chapter Nuclei. The main topics covered in Nuclei Class 12 notes are- The mass of the nucleus and its composition, Nuclear Binding Energy, Nuclear Force, Radioactivity, Nuclear Energy, Mass-Energy.
Nuclei Class 12 notes cover topics relevant to the CBSE Exam and can be downloaded from 12 Physics chapter 13 notes pdf download Class or from Nuclei pdf download. 12 Physics chapter 13 notes or notes for Class 12 Physics chapter 13 include basic equations as well. The necessary derivations are provided in CBSE Class 12 Physics chapter 13 notes. NCERT notes for Class 12 Physics chapter 13 are excellent for revision.
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Nucleus
In Rutherford’s ? particle scattering experiment, it showed that the whole positive charge and almost the whole mass of an atom are concentrated in an extremely small space at the centre of the atom this space is called the nucleus of the atom. The nucleus has protons and neutrons. The protons give a positive charge to the nucleus, while protons and neutrons together give it mass.
The neutron is uncharged, but its mass is nearly equal to the mass of a proton.
The total number of protons and neutrons is equal to the integral value of the atomic mass and is called the atomic mass number.
The number of protons is called the atomic number.
The atomic number of an atom is denoted by Z and mass by A, then its nucleus contains Z protons and ( A - Z ) neutrons. If the atomic no. of the atom X be Z and its mass no. be A then this atom is written as zXA.
The volume of a nucleus is directly proportional to the number of nucleons in it, which is its mass number A. Thus, if R is the radius of a nucleus then its volume is 4/3?R³.
Where R₀ is a constant. Experimentally its value is 1.2 х 10⁻¹⁵ m. Nuclei of different atoms have different radii.
Nuclear Shape
Nuclei are regarded as spherical.
Nuclear Density
The density of the nuclei of all atoms is almost the same. The density of nuclei is 2 × 10¹⁷kgm⁻³ which is 10¹³ to 10¹⁴ times the density of ordinary matter.
A small unit has been chosen to express the masses of atoms, nuclei and fundamental particles ( electrons, protons, etc.) called the ‘atomic mass unit’ and is denoted by u. 1 u is defined as one-twelfth part of carbon (₆C¹²) atom. According to this definition, the mass of carbon (₆C¹²) atom is exactly 12.00000...u
The mass of 1 gram-atom of carbon is 12 grams and it has N atoms, where N is Avogadro’s number. Thus the mass of one gram of carbon is 12/N gram. According to the definition,
But N = 6.02 × 10²³
The theory of relativity by Einstein proved that energy and mass are related to each other, and every substance has energy due to its mass also. If a substance loses an amount of Δm of its mass, an equivalent amount ΔE of energy is produced, where
Where c is the speed of light. This is called ‘‘Einstein’s energy-mass equivalence relation”.
If we give ΔE energy to some matter, then according to the above relation, its mass will increase by Δm, where
Since the value of c is very high, the increase in mass Δm is very small. The conversion of energy into mass and mass into energy can be observed at the nuclear level in the phenomena known as pair production and pair annihilation.
The difference between the mass and of the nucleons constituting a nucleus and the rest mass of the nucleus is called the mass defect Δm, i.e.,
Δm = (mass of protons + mass of neutrons ) - a mass of the nucleus
Let us consider an atom of an element zXA. Its atomic mass number is A and its atomic number is Z. Thus, its nucleus has Z protons and (A - Z) neutrons. If mp is the mass of a proton and mn the mass of a neutron and mN the mass of the nucleus, then the mass defect is
This equation means that when Z free protons and ( A - Z) free neutrons come in from infinity and combine together to form the nucleus, an amount of Δm mass disappears. The disappeared mass reappears as equivalent energy Δmc² which is liberated during the formation of the nucleus. It is due to this energy that protons and neutrons remain bound in the nucleus. Conversely, an amount Δmc² of external energy is required to break the nucleus into protons and neutrons. This is called the binding energy of the nucleus. Thus the Binding energy is defined as the minimum energy required to separate its nucleons and place them at rest at an infinite distance apart. Thus,
The electron binding energy is however negligible in comparison to the nucleon binding energy. Thus,
Putting the value of in eqn (i), we get
But the mass of hydrogen atom which contains one proton and one electron. Thus
This is the expression for the nuclear binding energy of an atom zXA in terms of atomic masses and neutron mass.
Eq (i) and Eq (ii) are identical because in eqn (ii) masses of Z electrons appear in the first and the second the first and third terms mutually cancel.
Since
the eq (ii) can also be written as
A graph between the average binding energy per nucleon and the mass number A of different nuclei is a curve called a Binding energy Curve.
(i) The curve is almost a flat maximum roughly from A = 50 to A = 80 corresponding to an average BE/nucleon of above 8.5 MeV. So, the nuclei having a mass number between 50 and 80 are stable.
(ii) for nuclei having mass numbers above 80 the average BE/nucleon decreases slowly and drops to about 7.6 MeV for Uranium.
(iii) for nuclei having mass numbers below 50 also the average BE/nucleon decreases and below 20 it decreases sharply this shows that the nuclei having mass numbers below 20 are comparatively less stable.
(iv) Below A = 50 the curve does not fall continuously but has subsidiary peaks at 8O16, 6C12 and 2He4. This shows that these (even-even )nuclei are more stable than their intermediate neighbours.
(v) The curve shows that very heavy and very light nuclei have a lower average BE/nucleon than the nuclei of intermediate masses. If a very heavy nucleus ( such as U238 ) Be separated into two lighter nuclei near the flat maximum of the curve, the BE/nucleon will increase by about 1 MeV. Hence energy will be released in the process. This method of releasing nuclear energy by breaking up a heavy nucleus into two lighter nuclei of comparable masses is called nuclear fission; it is the basis of nuclear bombs and nuclear reactors.
Alternatively, if two or more very light nuclei (such as H2) be combined to form a heavier nucleus ( such as He4), the BE/nucleon will again increase and now by a much greater amount than in the fission process. This will result in a much larger release of energy. This method of releasing nuclear energy is called nuclear fusion. It occurs inside the sun and other stars and is the source of their energy.
The nuclear force is stronger than the Coulomb force or the gravitational forces.
The nuclear force will become a repulsive force when the distance between two nucleons exceeds a few femtometers.
The nuclear forces between neutrons, proton-neutrons, and proton-protons are almost similar,
The spontaneous emission of rays from a substance is called Radioactivity and such a substance is called a radioactive substance.
By experiment, Rutherford observed that the radiation has three types of rays: one which deflected towards the negative plate, second which deflected towards the positive plate, and the third which one was undeflected in the electric field. These are called alpha rays (α-rays), ‘beta rays’ (β- rays), and gamma rays (γ- rays) respectively. α-rays and β- rays are streams of particles hence they are called α- and β- particles. α- and β- particles are positively charged and negatively charged respectively. The γ- rays are electrically neutral.
No radioactive substance emits both α- and β- particles simultaneously. Some substances emit α- particles and some others emit β- particles. γ- rays are emitted along with both α- and β- particles.
We know that a radioactive substance emits α- particles or β- particles and also γ- rays. The atomic weight and atomic number are changed. Thus, the original radioactive atom is decayed and an atom of some new element is born. This phenomenon is called “ Radioactive decay”.
For example when an α- particle is emitted from the uranium atom, then it is converted into a thorium atom.
Thorium is also radioactive and by emitting a β- particle, it is converted into a protactinium atom.
The radioactive decay continues until a stable atom is not obtained.
The rate of decay or disintegration of radioactive atoms is proportional to the number of atoms present at any given time.
Let N be the total number of atoms in a radioactive substance at any given time t.
Let dN be the no that disintegrates in a short interval dt. Then the rate of disintegration (- dN/dt) is proportional to N, i.e.,
? is a constant is known as decay constant.
On integrating,
C is constant. To determine C, apply the initial conditions. Let there are N₀ atoms, in the beginning, i.e., N = N₀ at t = 0. Then,
Putting this value in the above equation, we get
Here N₀ and N are the no. of the atoms in a radioactive substance at time t = 0 and after time t respectively. According to this eqn, the decay of radioactive substances is exponential.
Half-Life
The half-life of radioactive material is the time taken by it to decrease to half of its initial value. The half-life of a radioactive substance is constant, but it is different for different substances.
Relation between the half-life and decay constant
Let N₀ be the no. of atoms present in a radioactivity substance at time t =0 and be the no. at a later time t. Then
If the half-life of the substance be T, then at time t = T the no. of atoms left will be N₀ /2 so, on putting these values in the above eqn, we get
This is the relation between half-life and decay constant.
The activity of Radioactive substance
The number of decay or disintegration per second of a radioactive substance is called the activity ( R ) of the substance. I.e.,
the rate of decay of radioactive atoms at any instant is proportional to the number of atoms present at that instant.
Therefore, the activity of the substance at any instant is also proportional to the no. of its atoms left at that instant. Thus,
Initially, at t = 0, the no. of atoms in a substance is N₀, and the half-life of the substance is T. then after one half-life, the no. of atoms at t = T is
After two half-lives, the no. of atoms left will be N₀/4 i.e., t = 2T, the no. of atoms left is
Thus, the no. of atoms left after n half-lives is given by
The no. of atoms of a radioactive activity of a substance decreases with time (as shown in fig.)
The mean life of a radioactive substance is the expected life of the given sample. It is denoted by ?.
The reciprocal of the decay constant is the half life of a radioactive substance.
But
where T is the half-life of the substance.
Mean life is longer than half-life.
Alpha Decay
The emission of an Alpha particle from a radioactive nucleus is called Alpha decay it generally occurs in nuclei containing 210 or more nucleons. These new are so large that the short-range nuclear forces holding the nucleons together are unable to counterbalance the electrostatic repulsion among a large number of protons in them. Therefore in an attempt to achieve greater stability by reducing their size, they emit Alpha particles
Alpha particle is a helium nucleus whose atomic number is 2 and mass number is 4. Therefore when an Alpha particle is emitted from the nucleus of a radioactive atom the atomic number z decreases by 2 and the mass number decreases by 4. Thus the atom is converted into an atom of some other element. For example,
- decay is represented by the eqn
Since α- particle has high binding energy, its formation within the nucleus cause release of sufficient energy that becomes available to escape. The energy is shared by the daughter nucleus Y and the α-particle. Mostly the energy is taken by the α-particle.
Because an Alpha particle consists of two protons and neutrons, its emission from A nucleus b with the proton-neutron picture of the nucleus.
Beta Decay
Emission of aβ - particle from a radioactive nucleus is called beta decay. It generally occurs in nuclear having a neutron /proton ratio higher than that for stable nuclei.
At the time of emission of β-particle a neutron in the nucleus is converted into a proton and this process is a new particle and the new particle antineutrino is also originated. The emission is represented by the following equation
Since in β emission, a neutron is converted into a proton the neutron-proton ratio decreases
The antineutron is a particle of a zero rest mass and zero charge. Therefore, a beta particle is emitted from the nucleus of a radioactive atom and the atomic number Z (the number of protons) increases by one unit. But the total number of nucleons remains constant.. For example
Beta-decay is represented by the equation
Gamma decay
The emission ?-rays along with the emission of alpha or beta-particle, from a radioactive, is called gamma decay.
To explain the emission of Gamma rays from the nucleus it was assumed that as in an atom there are discrete energy levels within the nucleus also. When an Alpha or beta particle is emitted from the parent nucleus the daughter nucleus is left in an excited state the excited nucleus returns to its normal state by emitting its excess energy in the form of gamma rays.
For example, the unstable nucleus 27Co60 beta-decays to an excited nucleus 28Ni60 Which in turn reaches its stable ground state by emitting Gamma photons of energy 1.17 MeV and 1.33MeV into two ?-translation the existence of energy levels in the nucleus has been experimentally confirmed.
Nuclear fission is a process in which a heavy nucleus after capturing a neutron splits up into two lighter nuclei of comparable masses. The product nuclei are called fission fragments; the process is accompanied by the release of a few fast neutrons and a huge amount of energy in the form of the kinetic energy of the fission fragments and of the release of neutrons, Gamma rays, etc. Nuclear fission is the basis of nuclear bombs and nuclear reactors. For example-
When two or more very light nuclei moving at very high speeds are fused together to form a single nucleus then the process is known as nuclear fusion. The mass of the product nucleus is less than the sum of the masses of the nuclei which were fused. The lost mass is converted into energy which is released in this process. This property of light nuclei is shown by the binding energy curve in which the average binding energy per nucleon rises sharply with an increase in mass number in the range of low mass number nuclei. For example
Nuclear Reactor
A nuclear reactor is a device in which a self-sustaining controlled chain reaction is produced in fissionable material. It is thus, a source of controlled energy which is utilized for many useful purposes.
Nuclei Class 12 notes will be beneficial in revising the chapter and understanding the important topics. Also, these NCERT Class 12 Physics chapter 13 notes cover the main topics of the CBSE Class 12 Physics Syllabus and are helpful in preparation for competitive exams, including VITEEE, BITSAT, JEE MAIN, and NEET. Class 12 Physics chapter 13 notes pdf download is useful for preparing offline.
NCERT Class 12th Physics Chapter 13 Notes |
The main topics covered herein NCERT Class 12 Physics chapter 13 notes are Atomic masses and nuclei composition, Size of the nucleus, Mass-energy, Nuclear Binding Energy, Nuclear Force, Radioactivity, and Nuclear Energy.
The binding energy is defined as the minimum energy required to separate its nucleons and place them at rest at an infinite distance apart.
The spontaneous emission of rays from a substance is called radioactivity and such a substance is called a radioactive substance. It is an important topic from CBSE Class 12 Physics chapter 13 notes.
The half-life of radioactive material is the time taken by it to decrease to half of its initial value.
Students can expect 4 to 6 marks questions from the Class 12 Physics chapter 13 notes
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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.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
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.
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.
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
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
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