CBSE Class 12 Physics Revision Notes Chapter 12

Class 12 Physics Chapter 12 Notes – Atoms

Physics is the subject based on facts, assumptions, experiments, theories, numericals and interpretations. For students to get command over Physics, they need to be good in all these aspects. As a result, a detailed study of Physics is quite important for students to excel in their academics  as well as competitive examinations.

Atoms are the smallest unit of matter. You have studied the basics of atoms in your lower classes. You are already familiar with  the various theories by well-known scientists like Thomson, Rutherford, Neil Bohr etc. Let us gain some more information about atoms in this chapter. It will help you to go through different topics associated with it.

The important topics included in this chapter are the Alpha-particles scattering and the Rutherford model of the atom. You will get to know the observations, the conclusions and the limitations related to this model. You will also learn about the alpha-particle trajectory, electron orbits, atomic spectra, spectral series, Bohr model of the hydrogen atom, energy levels, the line spectra of the hydrogen atom and De-Broglie’s explanation of Bohr’s second postulate of quantisation.

It is one of the vital chapters of Physics. As a result, it is necessary for the students to have a clear understanding of this chapter. Extramarks Class 12 Physics Chapter 12 Notes include the entire chapter covered theoretically as well as practically in a detailed manner. Students can also find highlighted points and important formulas associated with the chapter listed in an organised manner. This will help them to revise the entire chapter quickly without taking too much of their  time.

They can get CBSE Class 12 Physics Chapter 12 Notes from the official website. Apart from this, Extramarks also provides comprehensive solutions for Classes 1 to 12 for all subjects. Its 360-degree learning pattern helps students to reinforce their conceptual understanding, and hence they must add  these notes in  study materials in order to perform well.

Key Topics Covered In Class 12 Physics Chapter 12 Notes

The study of atoms has always fascinated scientists and researchers for decades. It is considered the smallest unit of matter. But the detailed study interpreted that there are particles which are even smaller than atoms. These particles were named electrons, protons and neutrons. To know more about these particles and study the entire structure of the nucleus, scientists carried out various experiments. They put forward different theories to help us understand these charged particles better.

Chapter 12 Physics Class 12 Notes help us understand these topics and concepts in a more detailed way. You will learn about the important topics like Alpha-particle trajectory, Electron orbits, Atomic spectra, Spectral series, Bohr Model of the Hydrogen atom, Energy levels, the Line Spectra of the Hydrogen atom and De-Broglie’s Explanation of Bohr’s Second Postulate of Quantisation in this chapter. You will also get to know about Alpha-Particle Scattering and Rutherford’s Nuclear Model of the atom in this chapter.

Every aspect this chapter has been covered in the Class 12 Physics Chapter 12 notes. You can get it from the Extramarks official website and include it in your core study material in order to excel in your examinations and be a high level performer.

After completing the chapter, you can recall all the theories associated with different charge particles. You will be able to distinguish between electrons, protons and neutrons on the basis of their properties.

Introduction

This chapter covers one of the important topics of modern Physics called Atoms. An atom is composed of a nucleus which has protons and neutrons embedded in it. Protons are positively charged particles, and neutrons are neutrally charged particles. Electrons, the negatively charged particles, revolve around the nucleus in a fixed path called orbits. In short, an Atom is the miniature model of the planetary system. You will learn about many important concepts and theories in this chapter. These include

• Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom
• Alpha-particle trajectory
• Electron orbits
• Atomic Spectra
• Spectral series
• Bohr Model of the Hydrogen atom
• Energy levels
• The line spectra of the Hydrogen atom
• De-Broglie’s Explanation of Bohr’s Second Postulate of Quantisation

In Alpha-particles scattering and Rutherford’s Nuclear Model of the Atom, you would learn about the experiment carried out by Rutherford with the help of Alpha particles. Based on it, you would draw various observations and conclusions. You would also know about the limitations of this model.

In Alpha-particle trajectory, you will learn about energy produced in an atom through collision. The various types of collisions lead to strong energy generation in an atom which is used in the study of various fields of Physics. You will also get to know about the impact of Alpha particles on the scattering.

Like, the planets revolve around the sun in stationary orbits, in the same way, electrons revolve around the nucleus in the fixed orbits. These orbits are known as energy orbits. Rutherford gave his classical model in which the nucleus was present in the centre with positively charged protons and neutrally charged neutrons and electrons revolving around in the stable orbit.

Each element of the periodic table has individual spectra at which it emits radiations. This spectrum of radiation of different elements is known as atomic spectra. At specific spectra, the elements behave with particular wavelengths only. This is what you will learn in detail in this chapter.

The spectrum of light emitted by a particular element follows a certain pattern. These patterns are included in different spectral series. Spectral series include Balmer, Paschen, Pfund, Lyman etc. You will learn to calculate the wavelength in these series with the help of the formulas associated with it.

Neil Bohr gave the model of the hydrogen atom with the help of postulates. You will learn about each one of them in detail in this section. Additionally,  you will also learn various formulas associated with the Bohr model and will be able to use  them in the applications.

The energy of an electron is different at different energy levels. It has the least energy level when it is closest to the nucleus. The minimum energy level is found in the ground state. As we proceed to the higher energy level, the energy efficiency increases, and removing an electron becomes difficult. In this section, you will learn about the different energies associated with the electrons.

The Bohr Model of the Hydrogen atom explains more about the frequency of an electron during its transition from the higher energy level to the lower energy level. It helps us know about the hydrogen atom and its behaviour in detail.

De-Broglie re-explained Bohr’s second postulate of  quantisation with the help of experiments. Based on it, he gave certain conclusions which are of great help in studying modern Physics. You will learn more about it in this section.

Extramarks credibility lies in providing a reliable and trusted  study material related to NCERT from Class 1 to 12 for all the subjects.  One  can easily get access to the CBSE Class 12 Physics Chapter 12 Notes from the Extramarks’ website and  enjoy a better learning experience  and  enhance their performance  in the examinations. 

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

In 1911, Earnest, Rutherford and his students performed a critical experiment which showed that the Thompson Model might not be correct. 

They bombarded highly energetic α−Particles of the He−Nucleus onto a thin Gold foil. Following observations were drawn:

(i) Most of the particles passed through the foil as if it were an empty space.

(ii) Very few particles were even deflected backwards, fully reversing their direction.

(iii) Rest  were deflected and passed from 0° to 180° to the original direction of motion.

Conclusion: 

Rutherford gave the conclusion that most of the part of the atom is empty, and all the positive charge is concentrated at the centre in a very small volume. He named it the nucleus. 

Electrons move around the nucleus; likewise, the planets revolve around the sun. Thus, this model was also referred to as the planetary model of the atom.

Limitations: 

There were two basic problems with the model. They are as follows:

1. It could not give the cause for characteristic radiation coming from atoms. 
2. According to Maxwell’s theory of electromagnetic radiation, an orbiting electron has an accelerating charge. Hence, it should give out EM radiation resulting in the decrease of the radius of orbit and finally, it should fall on the nucleus. But the atom is a stable entity.

This section is merely based on the detailed study of the model of Rutherford. Hence, students should be completely aware of it . As a result, Extramarks has covered every bit of the section in the Class 12 Physics Chapter 12 Notes. You can get it from the official website.

Alpha-particle trajectory

The trajectory marked by an α-particle depends on the impact parameter of collision. The impact parameter is the perpendicular distance for the initial velocity vector of the α-particle from the centre of the nucleus. A given beam of α-particles has a distribution of impact parameters for the beam to scatter in various directions with different probabilities.

It is seen that an α-particle close to the nucleus suffers significant scattering. In a case of a head-on collision, the impact parameter is minimum, and the α-particle rebounds back (θ ≅ π). For a large impact parameter, the α-particle goes nearly undefeated and has a slight deflection (θ ≅ 0). The fact that only a tiny fraction of the number of incident particles rebound back indicates that the number of α-particles undergoing head-on collision is small. 

Thus, it implies that the mass and positive charge of the atom are concentrated in a small volume. Rutherford scattering, hence, is a powerful way to determine an upper limit to the size of the nucleus.

Alpha-particle trajectory is based on a few cases and certain assumptions which need to be understood very well. It has been included in-depth in the Class 12 Physics Chapter 12 Notes on the Extramarks’ website.

Electron orbits

The Rutherford nuclear model of the atom, which includes classical concepts, pictures the model of atom-like an electrically neutral sphere having a tiny, massive and positively charged nucleus at the centre surrounded by the revolving electrons in their respective dynamically stable orbits.

Hence, the relation between the orbit radius and the electron velocity is

r = e2 / 4.π.ε0.m.v2.

The kinetic energy (K) and the electrostatic potential energy (U ) of the electron in a hydrogen atom are given by

K = ½. mv2 = e2/8.π.ε0.r

also

U = -e2/4.π.ε0.r

 The negative sign in U shows that the electrostatic force is in the –r direction. As a result, the total energy E of the electron in a hydrogen atom is

E = K+U = e2/8.π.ε0.r – e2/4.π.ε0.r

An electron has the total energy negative. This helps us conclude the fact that the electron is bound to the nucleus. If E were positive, an electron would not revolve around a closed orbit around the nucleus.

This section is entirely based on solving numerical appropriately and using the concept of Electron orbits in the applications. You can find multiple questions to practice in the Class 12 Physics Chapter 12 Notes available on the Extramarks’ website.

Atomic Spectra

Each element has a characteristic spectrum of radiation, which it passes. When an atomic gas or vapour is excited at low pressure, usually by emitting an electric current through it, the emitted radiation has a spectrum which contains certain wavelengths only. 

A spectrum of such a kind is termed an emission line spectrum. It has a pattern of bright lines on a dark background. The study of emission line spectra of material can hence serve as a type of fingerprint for the identification of the gas. These dark lines correspond absolutely to those wavelengths which were found in the emission line spectrum of the gas. This is called the absorption spectrum.

Spectral series

The frequencies of the light given by a particular element would show some regular pattern. Hydrogen is the simplest atom. Hence, it has the simplest spectrum. 

In the observed spectrum, there was no resemblance seen in the order of regularity in the pattern of spectral lines. But the distance between these lines within specific sets of the hydrogen spectrum falls in a regular way. Each of these associated sets is called the spectral series. 

In 1885, the first such series was found in the visible region of the hydrogen spectrum. This series is called the Balmer series. Other series of spectra for hydrogen were consequently discovered. These are known, based on their discoverers, as the Lyman, Balmer, Paschen, Brackett, and Pfund series. 

The formulae represent these series:

Lyman series:

The spectral lines of the series correspond to the change of an electron from the higher energy state to the innermost orbit ( n=1, i.e. ground state). For the Lyman series, we get

n1= 1, n2 = 2,3,4,…

  1/ λ =R(1/12−1/n2); n=2,3,4,…

Balmer series: 

The spectral lines of the series correspond to the change of an electron from a higher energy state to an orbit having n=2.

For the Balmer series, we get, n1 = 2, n2 = 3,4,5,………

The wave numbers, as well as the wavelengths of spectral lines constituting the Balmer series, are given by:

             1/ λ =R(1/22−1/n2); for n=3,4,5,…

Paschen series:

The spectral lines of the series correspond to the change of an electron from the higher energy state to an orbit having n=3.

For the Paschen series, we get n1=3, n2=4,5,6,……

The wave numbers, as well as the wavelengths of spectral lines constituting the Paschen series, are given by

1/ λ  =R(1/32−1/n2); for n=4,5,6,…

Bracket series:

The spectral line of the series corresponds to the change of an electron from a higher energy state to the orbit having n=4.

For this series, we get, n1=4, n2=5.6,7,……

1/ λ  =R(1/42−1/n2); for n=5,6,7,…

Pfund series:

The spectral line of the series corresponds to the change of an electron from a higher energy state to the orbit having n=5.

For the series, we get n1=5 and n2=6.7,8,…….

The wave number, as well as the wavelength of the spectral lines constituting the Pfund series, are given by:

1/ λ  =R(1/52−1/n2); for n=6,7,8,…

The Lyman series lies in the ultraviolet region. The Paschen, Brackett, and Pfund series lie  in the infrared region. The Balmer series is found in the visible region.

While moving down to the ground state, an atom in the n=n state may give out a maximum (n-1) photons.

The first line of a series corresponds to the lowest energy photon given out, for e.g., the first line of the Balmer series corresponds to the change from n=3 to n=2.

The Series limit corresponds to the maximum energy photon given out, e.g. series limit of the Balmer series corresponds to the change from n=∞ to n=2.

The maximum number of lines in the emission spectrum of a gas which is to a higher level 

n=n will be n(n-1) / 2.

For an atom in the quantum state n=n,

• Maximum energy photons will be given out for a change from n=n to n=1.
• Minimum energy photons will be given out for a change from n=n to n=-1.

The knowledge of various series of the  atomic spectra is essential for the proper understanding of the chapter. Hence, we have discussed everything related to it  in detail  in the Class 12 Physics Chapter 12 Notes available on the Extramarks’ website.

Bohr Model of the Hydrogen atom

Bohr explained the first successful picture of the atom. His model successfully shows the lines of EM radiation coming out from H2 – gas. Although it is now considered vague and has been completely replaced by the Quantum Mechanical Theory, it was historically important to the development of Quantum Mechanics.

Earlier Bohr combined various  quantum concepts and thereby gave his theory in the form of three postulates. They are : 

(i) According to Bohr’s first postulate, an atom could revolve in certain stable orbits without the emission of radiant energy, which is contrary to the predictions of electromagnetic theory. Each atom has certain definite stable states in which it exists. Each possible state has definite total energy. These are called the stationary states of the atom. 

(ii) According to Bohr’s second postulate, the electron revolves around the nucleus only in the orbits, which have the angular momentum is some integral multiple of h/2π, where h is the Planck’s constant (= 6.6 × 10–34 J s). Therefore, the angular momentum (L) of the orbiting electron is quantised. 

Then, 

L = nh/2π  

(iii). According to Bohr’s third postulate, an electron might change from one of its specified non-radiating orbits to another of lower energy. He combined atomic theory with the early quantum concepts that Planck and Einstein had developed.

When this happens, a photon is given out having energy that is equal to the energy difference between the initial and final states. The frequency of the so-called emitted photon is given by 

hν = Ei – Ef

Here,. Ei and Ef are the energies of the initial and final states, and Ei> Ef.

The atomic energies for the electron in joules are given by:

En = − (2.18 x 10-18/n2) J

Atomic energies are expressed in electron volts (eV) rather than joules. It can also be written as 

En = − (13.6/n2) eV.

The total energy of the electron has a negative sign when it is revolving in an orbit, which means that the electron is close to the nucleus. Energy will be needed to remove the electron from the hydrogen atom to a distance infinitely far from its nucleus.

The essential formulas associated with the Bohr Model of Hydrogen atom are:

 (i) Radius in nth orbit, for rn= (n2h2ϵ0) / (Ze2πm) = (0.53   Å)n2/z

(ii) Speed of electron in nth orbit, for vn = ze2/ 2nhϵa = (2.18 × 106 m s−1)z/n

 (iii) for H-atom,

(a) Radius of 1st orbit for ,r1 = 0.53 Å,

(b) speed of electron in 1st orbit, for v1=2.18 × 106 m s−1

(iv) Kinetic energy of electron nth orbit, 

KE = 1/2mv2 = ½ {ze2 / 2ϵ0nh}2

Then,

KEn=1/2[mz2e4/4ϵ02n2h2]  ∝ z2n2

(v) Potential energy of for electron: For the electric field of the nucleus, the PE of the electron in the nth orbit can be written as, 

Un = [1/4πϵ0](ze)(−e)/r

Also,

Un=−[mz2c4/4εo2n2h2] ∝ z2n2

The negative sign implies that the electron is close to the nucleus, and some work is needed to remove it from the nucleus.

(vi) Expression for the total energy of an electron in the nth orbit,

Can be written as;

En = KEn + Un = −1/2[mz2c4/4εo2n2h2] ∝ z2n2

(vii) From the general expression of total energy, 

We get, 

En=−[me4/8 εo2h3c]hc(z2/n2) Or En=−(Rhc) z2/n2  here R=me4/8 εo2h3 is called the Rydberg constant.

R=1.097×107 m−1

‘Rhc’ is said to be Rydberg Energy =13.6 eV.

All the essential concepts, theories, facts, formulas, assumptions and numerals are covered in detail in the Class 12 Physics Chapter 12 Notes on the Extramarks’ website. 

Energy levels

The energy of an atom is minimum when the electron moves in orbit nearest to the nucleus, i.e., the one for which the n = 1. For n = 2, 3, 4… the absolute value of the energy E is smaller.

Hence, the energy is comparatively larger in an outer orbit. The lowest state of the atom, known as the ground state, is that of the lowest energy, with the electron revolving in the orbit of the smallest radius, for the Bohr radius, a0. The energy of this state for (n = 1), 

E1 is –13.6 eV. 

Hence, the minimum energy necessary to free an electron from the ground state of the hydrogen atom is 13.6 eV. This is called the ionisation energy of the hydrogen atom. Thus, the prediction of Bohr’s model perfectly agrees with the experimental value of ionisation energy.

Most of the hydrogen atoms are found in the ground state at room temperature. When a hydrogen atom gets energy by processes such as electron collisions, the atom may acquire sufficient energy to lift up the electron to higher energy states. The atom is called an excited state. For n = 2, we can observe that the energy 

E2 is –3.40 eV. 

It means that the energy required to excite an electron in a hydrogen atom to its first excited state equals 

 E2 – E1 = –3.40 eV – (–13.6) eV 

                                = 10.2 eV. 

Similarly, E3 = –1.51 eV and E3 – E1 = 12.09 eV, or to excite the hydrogen atom from its ground state (n = 1) to a second excited state (n = 3), 12.09 eV energy is required, and so on. 

The electron can then fall back to a state of lower energy from these excited states, giving a photon in the process. Thus, as the excitation of the hydrogen atom increases (that is, as n increases), the value of minimum energy required to free the electron from the excited atom decreases.

The principal quantum number ‘n’ labels the stationary states in the increasing order of energy. The highest energy state corresponds to n =∞ and has an energy of 0 eV. 

This is the energy of the atom when an electron is entirely removed (r = ∞) from the nucleus and is at rest. You can observe how the energies of the excited states come closer and closer together as n increases.

Binding Energy of a state: Energy required to remove the electron from a particular quantum state is called BE of that particular state.

Ionisation energy: The energy required to remove an electron from the atom’s ground state is called its ionisation energy.

Ionisation Potential: The Potential difference through which an e must be accelerated to acquire this much energy (i.e. ionisation energy) is called ionisation Potential.

Excitation energy: The energy which must be provided to the e of the atom so that it may go to a higher energy level is called excitation energy of that excited state. For the equation for H-atom.

Excitation Potential: The Potential difference through which an e must be accelerated to acquire this much energy (i.e. excitation energy) is called excitation Potential.

The various definitions related to energy, their properties, the behaviour of an atom at different energy levels, their applications and all the terminologies are covered in the Class 12 Physics Chapter 12 Notes available on the Extramarks’ website.

The Line Spectra of the Hydrogen Atom

 As per the third postulate of Bohr’s model, when an atom transitions from the higher energy state with quantum number ni to the lower energy state with quantum number nf (nf < ni ), the difference in energy is taken away by a photon of frequency νg.

Since both nf and ni are integers, this immediately shows that light is given in different discrete frequencies in changes between different atomic levels. 

For hydrogen spectrum, the Balmer formula corresponds to nf = 2 and ni = 3, 4, 5, etc. The outcome of Bohr’s model suggested the presence of other series spectra for the hydrogen atoms.

Those correspond to transitions resulting from nf = 1 and ni = 2, 3, etc.; nf = 3 and ni = 4, 5, etc., and so on. Such series were recognised in the course of spectroscopic investigations and are known as the Lyman, Balmer, Paschen, Brackett, and Pfund series.

The various lines in the atomic spectra are produced when electrons jump from a higher energy state to a lower energy state and photons are emitted. These spectral lines are called emission lines.

A hydrogen atom behaves differently at different energy levels. The behaviour is also associated with the various series. You will find the properties of an electron and proton in the Class 12 Physics Chapter 12 Notes available on the Extramarks’ website.

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

Einstein explained that light behaves both as a matter particle as well as a wave. De-Broglie extended Einstein’s view and said that all forms of matter, like electrons, protons, neutrons etc., also have a dual character. He further said that wavelength ‘λ’ associated with a particle of mass ‘m’ moving with velocity ‘v’ is given by

         λ = h/mv = h/p, 

where λ is called de Broglie’s wavelength.

Further, if the moving particle’s KE is K, then 

λ=h/√(2mK).

If a charged particle  ‘q’ is accelerated through a potential difference ΔV, then 

λ = h√[2mq(ΔV)].

An electron behaves as a standing or stationary wave, which extends around the nuclei in a circular orbit. If the two ends of the electron wave meet to give a regular series of crests and troughs, the electron wave is said to be in phase. i.e., there is constructive interference of electron waves, and the electron motion has the character of a standing wave or non-energy radiation motion.

Whatever be the path of the electron wave around the nucleus, it is necessary to get an electron wave in phase so that the circumference of the Bohr’s orbit (=2πr) is equal to the whole number multiple to wavelength λ of the electron wave. In each case, a whole number of wavelengths fill the circumference of the loop.

2πr = nλ or λ = 2πr/n, 

Where  ‘n’  is a whole number which denotes the number of wavelengths associated with an electron wave extending around the nucleus. 

Now according to De – Broglie,

λ = h/mv. 

 Hence, we get

2πr/n = h/mv or mvr =  nh/2π.

An electron revolving in a proper orbit does not radiate energy, though it is accelerating. So, the total energy of the electron remains constant. That is why the permitted orbits are also called stationary or non-radiating orbits.

Summary

1. The atom, as a whole part, is electrically neutral and therefore contains an equal amount of positive and negative charges. 
2. In Thomson’s model, an atom is a spherical cloud of positive charges with electrons embedded in it.
3. In Rutherford’s model, most of the atom’s mass and all its positive charge is concentrated in a tiny nucleus (typically one by ten thousand, the size of an atom), and the electrons revolve around it.
4. Rutherford’s nuclear model has two main difficulties in explaining the structure of atoms.

(a) It assumes that atoms are unstable because the

accelerated electrons revolving around the nucleus must spiral into the nucleus. This is contrary to the stability of matter. 

(b) It cannot explain the characteristic line spectra of atoms of different elements. 

5. Most elements’ atoms are stable and emit a characteristic spectrum. The spectrum consists of a set of isolated parallel lines termed line atomic structure spectrum. It gives useful information about the atomic structure.
6. The atomic hydrogen gives a line spectrum having different series. The frequency of any line in a series can be expressed as a difference between two terms: 

Lyman series:               

1/ λ =R(1/12−1/n2); n=2,3,4,…

Balmer series:

1/ λ =R(1/22−1/n2); n=3,4,5,…

Paschen series: 

 1/ λ  =R(1/32−1/n2); n=4,5,6,…

Brackett series:

1/ λ  =R(1/42−1/n2); n=5,6,7,…

7. To explain the line spectra emitted by atoms and the stability of atoms, Niels Bohr proposed a model for hydrogenic (single electron) atoms. He introduced three postulates and laid the foundations of quantum mechanics.

(a) In a hydrogen atom, the electron moves in certain stable orbits (called stationary orbits) without emitting radiant energy.

(b) The stationary orbits are for which the angular momentum is some integral multiple of h/2πr, i.e. L = nh/2πr, where n is an integer known as the principal quantum number. 

(c) The third postulate states that an electron might change from one of its specified non-radiating orbits to another of lower energy. When this happens, a photon is given energy equal to the energy difference between the initial and final states. Hv = Ei-Ef then gives the frequency (v) of the emitted photon.

An atom absorbs radiation of the identical frequency the atom gives out, in which case the electron is transferred to an orbit with a higher value of n.

Ei+ hv=Ef

Due to the quantisation condition of angular momentum. The electron orbits the nucleus at only certain radii.

E= =-13.6 eV/m²

The n = 1 state is called ground state. In a hydrogen atom, the ground state energy is -13.6 eV. 

Higher values of n correspond to excited states for which (n> 1). Atoms are excited to these higher states by collisions with other atoms or electrons or by absorption of a photon of the right frequency.

9. De-Broglie’s hypothesis that electrons have a wavelength λ=h/mv explained Bohr’s quantised orbits by bringing in the wave-particle duality. The orbits relate to circular standing waves for which the circumference of the orbit equals the whole number of wavelengths. 
10. Bohr’s model is applied only to hydrogenic (single electron) atoms. It cannot be extended to even two-electron atoms such as helium. This model can also not explain the relative intensities of the frequencies emitted by hydrogenic atoms.

The  entire chapter is covered in detail in the Class 12 Physics Chapter 12 Notes available on the Extramarks’ website.

Class 12 Physics Chapter 12 Notes: Exercise &  Solutions

To brush up your knowledge and get results to the fullest, you must have the right solutions to all the exercises given in the NCERT Class 12 Physics textbook. The solutions should be accurate, precise  and it must be written by experienced subject matter experts. . Keeping this in mind, Extramarks provides Class 12 Physics Chapter 12 Notes to all its students.

Extramarks provides the best learning  material  after a thorough analysis  and designed as per the CBSE curriculum. Students can get the Class 12 Physics Chapter 12 Notes from Extramarks’ official website to maximise their potential  and make the most of it.

Click on the  links given below to view exercise-specific questions and solutions covered in our Class 12 Physics Chapter 12 Notes

• Class 12 Physics Chapter 12: Exercises – Questions and Answers

Along with Class 12 Physics Chapter 12 Notes, students can explore other study materials for the CBSE Syllabus by selecting the links given below:

• NCERT Books
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NCERT Exemplar Class 12 Physics

NCERT Exemplar Class 12 Physics book has a collection of all NCERT-related questions. The benefits provided in this book will overall make a difference in their academic performance.   Students can step up  their practice and revision if they have access to a set of questions designed as per their curriculum. NCERT Exemplar Class 12 Physics covers all these aspects which boost students’ confidence during their preparation.

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Students can ensure guaranteed success once they include Class 12 Physics Chapter 12 Notes and NCERT Exemplar Class 12 Physics in their study material. This will aid students in solving all types of questions confidently, helping them develop an interest in the subject at large. This way, they can let go of their  fear of examinations and be confident..

Key Features of Class 12 Physics Chapter 12 Notes

 Students can get  good grades in Physics, only if  they clear their doubts and have conceptual clarity. Hence, Class 12 Physics Chapter 12 Notes focuses on the subjective as well as an objective understanding of the students. The key features are as follows: 

• All the theoretical as well as practical  concepts are covered in detail  for the students to have a strong fundamental base  and are able to solve advanced level questions from the chapter. .
• Students will build subjective and objective knowledge and be able to handle tweaked CBSE questions in the board exams with ease and come up with accurate answers. .
• After referring to Class 12 Physics Chapter 12 Notes, students will  find  the chapter ‘Atoms’ comparatively easier  and can interrelate all the concepts learnt in the lower classes.