# NCERT Solutions for Class 12 Physics Chapter 12 Atoms

**NCERT Solutions for Class 12 Physics Chapter 12 Atoms: **Do you know that an atom is electrically neutral, which tells that atoms contain an equal number of positive and negative charges. The Atoms Class 12 NCERT Solutions explain questions related to different models of the atom, their drawbacks, hydrogen spectra, and Debroglie hypothesis. CBSE NCERT solutions for Class 12 Physics chapter 12 atoms will help you in board exam preparation. The solutions of NCERT plays a major role in making the concepts easy and hence will help in competitive exams also. The questions in Atoms Class 12 NCERT text book are divided in to exercise and additional exercise. All questions are solved based on the NCERT syllabus.

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Studying NCERT solutions for Class 12 Physics Chapter 12 Atoms is important because it provides a clear and detailed understanding of the questions covered in the chapter. It also helps in preparing for exams like JEE or NEET and understanding the fundamental principles of physics.

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** NCERT Solutions for Class 12 Physics Chapter 12 Atoms exercise: **

** Q 12.1 ** Choose the correct alternative from the clues given at the end of the each statement:

(a) The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model. (much greater than/no different from/much less than.)

(b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomson’s model/ Rutherford’s model.)

(c) A classical atom based on .......... is doomed to collapse. (Thomson’s model/ Rutherford’s model.)

(d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomson’s model/ Rutherford’s model.)

(e) The positively charged part of the atom possesses most of the mass in .......... (Rutherford’s model/both the models.)

** Answer: **

(a) The size of the atom in Thomson’s model is __ no different from __ the atomic size in Rutherford’s model.

(b) In the ground state of __ Thomson’s model __ electrons are in stable equilibrium, while in __ Rutherford’s model __ electrons always experience a net force.

(c) A classical atom based on __ Rutherford’s model __ is doomed to collapse.

(d) An atom has a nearly continuous mass distribution in a __ Thomson’s model __ but has a highly non-uniform mass distribution in __ Rutherford’s model __ .

(e) The positively charged part of the atom possesses most of the mass in __ both the models __ .

** Answer: **

On repeating the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil we would have different observations than Rutherford, as the alpha particles won't be scattered much because of being heavier than the nucleus of the Hydrogen atom. Therefore we would not be able to confirm the presence of almost the entire mass of the atom at its centre.

** Q 12.3 ** What is the shortest wavelength present in the Paschen series of spectral lines?

** Answer: **

The Rydberg's formula for the hydrogen atom is

Where R is Rydberg constant for the Hydrogen atom and equals to 1.1 10 ^{ 7 } m ^{ -1 }

For shortest wavelength in Paschen Series n _{ 1 } =2 and n _{ 2 } =

The shortest wavelength in Paschen Series is therefore 818 nm.

** Answer: **

Frequency of radiation consisting of photons of energy E is given by

E=2.3 eV

Plank's constant(h)=6.62 10 ^{ -34 } Js

** Answer: **

The ground state energy E=-13.6 eV.

The kinetic energy= -E=13.6 eV

Also ground state energy = Kinetic energy+Potential energy

E=K+U

U=E-K

U=-13.6-13.6

U=-27.2 eV

The kinetic and potential energies are 13.6 eV and -27.2 eV respectively.

** Answer: **

The initial energy of the electron is E _{ 1 }

E _{ 1 } =-13.6 eV

The energy of the electron when it is excited to level n=4 is E _{ 2 }

E _{ 2 } =-0.85 eV

The difference between these two energy levels is equal to the energy of the photon absorbed by the electron.

The energy of the photon E = E _{ 2 } - E _{ 1 }

E = -0.85 -(-13.6)

E = 12.75 eV

The wavelength of the photon can be calculated using relation

hc=1240 eV

The wavelength and frequency of the photon absorbed by the hydrogen atom are 98.6 nm and 3.04 10 ^{ 15 } Hz respectively.

** Answer: **

As per Bohr's model the angular momentum of electrons in each orbit is constant and a multiple of

(i)

The electrostatic force of attraction between the electron and the nucleus provides the required centripetal force for the circular motion of the electron.

(ii)

Using equation (i) and (ii) we get

v _{ 1 } =2.18 10 ^{ 6 } ms ^{ -1 }

v _{ 2 } =1.09 10 ^{ 6 } ms ^{ -1 }

v _{ 3 } =7.28 10 ^{ 5 } ms ^{ -1 }

** (b) ** calculate the orbital period in each of these levels.

** Answer: **

Orbital period (T _{ n } ) is defined as time taken by the electron to complete one revolution around the nucleus and is given by

T _{ 1 } =1.53 10 ^{ -16 } s

T _{ 2 } =1.22 10 ^{ -15 } s

T3=4.12 10 ^{ -15 } s

** Answer: **

The radius of the orbit is proportional to the square of n.

For n=2 the radius of the orbit is

For n=3 the radius of the orbit is

** Answer: **

Since the energy of the electron beam is 12.5 eV the Hydrogen atoms will get excited to all requiring energy equal to or less than 12.5 eV

E _{ 1 } =-13.6 eV

E _{ 3 } = -1.5 eV

E _{ 3 } -E _{ 1 } = 12.1 eV

E _{ 4 } = -0.85 eV

E _{ 4 } -E _{ 1 } =12.75 eV

Therefore the electron can reach maximum upto the level n=3.

During de-excitations, the electron can jump directly from n=3 to n=1 or it can first jump from n=3 to n=2 and then from n=2 to n=1

Therefore two wavelengths from the Lyman series and one from the Balmer series will be emitted

To find the wavelengths emitted we will use the Rydberg's Formula

where R is the Rydberg's constant and equals 1.097 10 ^{ 7 } m ^{ -1 }

For n _{ 1 } =1 and n _{ 2 } =3

Emitted wavelength is 102.5 nm

For n _{ 1 } =1 and n _{ 2 } =2

Emitted wavelength is 121.54 nm

For n _{ 1 } =2 and n _{ 2 } =3

Emitted wavelength is 656.3 nm

** Answer: **

As per the Bohr's model, the angular of the Earth will be quantized and will be a multiple of

n = 2.56 10 ^{ 74 }

Therefore the quantum number that characterises the earth’s revolution around the sun in an orbit of radius m with an orbital speed

is 2.56 10 ^{ 74 }

## ** NCERT solutions for class 12 physics chapter 12 atoms additional exercise: **

Is the average angle of deflection of -particles by a thin gold foil predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?

** Answer: **

The average angle of deflection of -particles by a thin gold foil predicted by both the models is about the same.

Is the probability of backward scattering (i.e., scattering of -particles at angles greater than ) predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?

** Answer: **

The probability of backward scattering predicted by Thomson’s model is much less than that predicted by Rutherford’s model.

Keeping other factors fixed, it is found experimentally that for small thickness t, the number of -particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

** Answer: **

Scattering at moderate angles requires head-on collision the probability of which increases with the number of target atoms in the path of -particles which increases linearly with the thickness of the gold foil and therefore the linear dependence between the number of -particles scattered at a moderate angle and the thickness t of the gold foil.

In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of -particles by a thin foil?

** Answer: **

It is completely wrong to ignore multiple scattering for the calculation of the average angle of scattering of -particles by a thin foil in Thomson's model as the deflection caused by a single collision in this model is very small.

** Answer: **

As per the bohrs model

(i)

If the proton and the electron were bound only by the gravity the gravitational force between them will provide the centripetal force required for circular motion

(ii)

From equation (i) and (ii) we can calculate that the radius of the ground state (for n=1) will be

The above value is larger in order than the diameter of the observable universe. This shows how much weak the gravitational forces of attraction as compared to electrostatic forces.

** Answer: **

Using Bohr's model we have.

Since n is very large 2n-1 can be taken as 2n and n-1 as n

The frequency of the emission caused by de-excitation from n to n-1 would be

The classical frequency of revolution of the electron in the nth orbit is given by

The above is the same as the frequency of the emission during de-excitation from n to n-1.

(a) construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.

** Answer: **

Using dimensional analysis we can see that the quantity to be constructed and consisting of m _{ e } , e and c will also have and will be equal to

and has numerical value 3.5 10 ^{ -14 } which is much smaller than the order of atomic radii.

(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

** Answer: **

Using dimensional analysis we can see that the quantity to be constructed and consisting of m _{ e } , e and h will also have and will be equal to

and has a numerical value of approximately 6.657 10 ^{ -10 } which is about the order of atomic radii.

** Q 12.15 ** ** (a) ** The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV.

What is the kinetic energy of the electron in this state?

** Answer: **

Since we know that kinetic energy is equal to the negative of the total energy

K=-E

K=-(-3.4)

K=3.4 eV

** Q 12.15 ** ** (b) ** The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV.

What is the potential energy of the electron in this state?

** Answer: **

Total Energy= Potential energy + Kinetic Energy

E=U+K

U=E-K

U=-3.4-3.4

U=-6.8 eV

** Q 12.15 ** ** (c) ** The total energy of an electron in the first excited state of the hydrogen atom is about - 3.4eV.

Which of the answers above would change if the choice of the zero of potential energy is changed?

** Answer: **

The total energy would change if the choice of the zero of potential energy is changed.

** Answer: **

We never speak of Bohr's quantization postulate while studying planetary motion or even motion of other macroscopic objects because they have angular momentum very large relative to the value of h. In fact, their angular momentum is so large as compared to the value of h that the angular momentum of the earth has a quantum number of order 10 ^{ 70 } . Therefore the angular momentum of such large objects is taken to be continuous rather than quantized.

** Answer: **

As per Bohr's quantization postulate

Similarly, like the case in a simple hydrogen atom, the electrostatic force acts centripetally

From the above relations, we can see that in Bohr's model the Radius is inversely proportional to the mass of the orbiting body and Energy is directly proportional to the mass of the orbiting body.

In case of hydrogen, atom r _{ 1 } is 5.3 10 ^{ -11 } m

Therefore in case of a muonic hydrogen atom

r _{ 1 } = 2.56 10 ^{ -13 } m

In case of the hydrogen atom, E _{ 1 } is -13.6 eV

Therefore in case of a muonic hydrogen atom

E _{ 1 } =207 (-13.6)

E _{ 1 } =2.81 keV

**Key Features Of Atoms Class 12 NCERT Solutions**

Atoms Class 12 comes under the unit Modern Physics. There are a seventeen questions discussed in the NCERT solutions for Class 12 Physics Class 12 Chapter 12 Atoms. Some of the important formulas of the chapter atoms which will help in NCERT solutions for class 12 physics are given below.

- According to Bohr’s postulates for stationary orbit angular momentum

Where n is the quantum number

The total energy of the electron in the stationary states of the hydrogen atom in electronvolt is given by

Another important formula in NCERT is the

De Broglie wavelength

Where ‘h’ is Planck's constant and mv is the momentum. This relation can be modified in terms of the kinetic energy of the particle. Try to derive it yourself.

** ****NCERT solutions for class 12 physics chapter wise **

** NCERT solutions subject wise **

- NCERT solutions for class 12 mathematics
- NCERT solutions for class 12 chemistry
- NCERT solutions for class 12 physics
- NCERT solutions for class 12 biology

## ** Importance of NCERT solutions for class 12 physics chapter 12 atoms: **

For CBSE board exam on an average 3 to 4 marks questions are asked from the chapter Atoms. The solutions of NCERT Class 12 Physics chapter 12 Atoms will help in securing full marks in board exam for this chapter. As far as the NEET exam is considered up to 2 questions are expected from the chapter Atoms Class 12 Physics. The NCERT solutions for Class 12 Physics chapter 12 atoms will also help to perform better in exams like JEE Main and other competitive exams.

## Some of the important topics covered in Class 12 Physics Chapter 12 Atoms are:

De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation

Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom

Alpha-particle Trajectory

X-rays

Bohr Model of the Hydrogen Atom

The Line Spectra of the Hydrogen Atom

These topics are the main focus of the NCERT textbook and are likely to be given more emphasis in exams.

### Also Check NCERT Books and NCERT Syllabus here:

- NCERT Books Class 12 Physics
- NCERT Syllabus Class 12 Physics
- NCERT Books Class 12
- NCERT Syllabus Class 12

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 12 Physics Chapter 12 Atoms

**Question: **What do you mean by according to class 12 physics chapter 12 ncert solutions?

**Answer: **

Atomic spectra refer to the unique set of lines or bands emitted or absorbed by an atom when it is excited, they are used to identify elements and study the properties of atoms and their electronic structure. The study of atomic spectra is known as spectroscopy.

**Question: **How class 12 physics atom is important for NEET?

**Answer: **

class 12 physics atom is important for NEET because it forms the foundation of many important concepts in chemistry and physics, including atomic structure, quantum mechanics, wave-particle duality, chemical bonding, and the properties of chemical compounds.

**Question: **What are the important topics of the Class 12 NCERT chapter Atoms

**Answer: **

The Hydrogen spectrum, Energy of atoms, Bhor Model of Atom, Bhor Postulates etc are important topics of the Atoms Class 12 Physics Chapter. More questions related to these topics an be practiced from NCERT Exemplar for Class 12 Physics.

**Question: **What is the importance of the chapter for engineering and medical entrance exams?

**Answer: **

The Class 12 Physics chapter Atoms are important for both engineering and medical exams. At least one question can be expected from Atoms for both JEE Main and NEET.

**Question: **How many questions from the chapter atoms comes in CBSE board exams?

**Answer: **

One or two questions are usually asked in the CBSE board exams from Class 12 chapter Atoms. It can be a 2 or 3 mark question. Students should cover all the concepts of the Class 12 chapter Atoms. The question may be theoretical, numerical or derivations. The syllabus of CBSE board is based on the NCERT book. Students can practice questions based on NCERT syllabus for the board exam.

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## Questions related to CBSE Class 12th

### i couldnt clear 1st compartment (which held in August 2022) cbse class 12th so can I give improvement in all subjects which to be held on March 2023. tell me a solution i need more than 75% in 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

### i was not able to clear 1st compartment and now I have to give 2nd compartment so can I give improvement exam next year? plz tell me very much tensed(cbse class 12th)

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.

### if i am giving improvement in one subject this year, will i be able to give improvement in more subjects next year?

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.

### I got an RT for 2 subjects, so do I have to give exams for all the subjects in the coming year or just the 2. pls help me

Hi,

You just need to give the exams for the concerned two subjects in which you have got RT. There is no need to give exam for all of your subjects, you can just fill the form for the two subjects only.

### I will have my boards in Feb 2023 (Class 12) and I still havent completed 1 chapter in any subject (Physics, chemistry and maths) , My 11th concepts are not that great but its okish, I wanted to know that If I do start studying from 15th of August Can I get above 85?

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.