Skip to content
← Physics

Physics · Class 12 Science

Ch 8Atomic and Nuclear Physics — Class 12 Physics, concept-first.

Everything around us that occupies space is matter, and matter appears in the forms solid, liquid and gas. Different materials behave very differently from one another - water, petrol, oxygen, stainless steel - and to understand why their physical and chemical properties differ, physicists needed to identify the fundam…

127

Q&A

32

Concepts

~7m

Unit weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

8.1

Introduction

Everything around us that occupies space is matter, and matter appears in the forms solid, liquid and gas.

8.2

Electric Discharge Through Gases

Under normal atmospheric conditions, gases are poor conductors of electricity because they contain essentially no free electrons available to carry current.

8.2.1

Determination of specific charge e/m of an electron - Thomson's experiment

J.J. Thomson's 1887 experiment measured the "specific charge" of the electron - its charge-to-mass ratio - and is regarded as one of the landmark experiments marking the birth of modern physics.

8.2.2

Determination of charge of an electron - Millikan's oil drop experiment

Once the specific charge of the electron was known from Thomson's experiment, the next step was to measure the electron's actual charge itself. This was accomplished by R.A.

8.3

Atom Models

Around 400 BC, the Greek philosophers Leucippus and Democritus first proposed that matter, if repeatedly subdivided, would eventually yield indivisible atoms.

8.3.1

J.J. Thomson's Model (Water melon model)

J.J. Thomson's 1904 atom model - nicknamed the "watermelon model" - pictures the atom as a homogeneous sphere of uniformly distributed positive charge, with the negatively charged electrons embedded i…

8.3.2

Rutherford's model

In 1911, acting on Rutherford's advice, his students Hans Geiger and Ernest Marsden carried out what became one of the most famous experiments in physics: firing alpha particles at a thin gold foil an…

(A)

Distance of closest approach

When an alpha particle is aimed exactly at the centre of a nucleus (a head-on collision), it slows down continuously as the repulsive Coulomb force from the positively charged nucleus grows stronger,…

(B)

Impact parameter

Not every alpha particle in Geiger and Marsden's beam was aimed exactly at a gold nucleus's centre - most missed by some offset distance, which is what produces the whole range of observed scattering…

8.3.3

Bohr atom model

To overcome Rutherford's twin failures - instability and continuous emission - Niels Bohr introduced quantisation into the atomic model. His postulates for the hydrogen atom are:

8.3.4

Atomic spectra

Heated solids, liquids and gases generally emit a continuous spectrum of electromagnetic radiation - all wavelengths represented, as seen when white light is passed through a spectrometer.

8.4

Nuclei

Having discussed the theoretical models of the atom as a whole in the previous sections - Thomson's watermelon model, Rutherford's alpha-scattering-derived nuclear model, and Bohr's quantised orbital…

8.4.1

Composition of nucleus

The nucleus at the centre of every atom is built from two kinds of particles, collectively called nucleons: protons, which carry a positive charge (equal in magnitude to the electron's charge), and ne…

8.4.2

Isotopes, isobars, and isotones

Nuclei can be classified and compared along three different axes, depending on which of , or they share:

8.4.3

Atomic and nuclear masses

Nuclear masses, expressed in kilograms, are inconveniently tiny numbers (of order kg or smaller), so it is far more practical to use a specially defined unit called the atomic mass unit (u).

8.4.4

Size and density of the nucleus

The alpha-particle scattering experiment, together with many other independent measurement techniques applied to a wide range of nuclei, shows that nuclei are approximately spherical, and that for nuc…

8.4.5

Mass defect and binding energy

A remarkable experimental fact underlies the entire concept of nuclear binding energy: the measured mass of any nucleus is always slightly less than the sum of the masses of its individual, separated…

8.4.6

Binding energy curve

Rather than just the total binding energy of a nucleus, it is far more informative to compute the average binding energy per nucleon, which represents, roughly, the energy needed to pull a single typi…

8.5

Nuclear Force

Since like charges repel, and protons inside a nucleus are packed only a few fermi ( m) apart, simple electrostatics predicts an enormous mutual repulsion between them.

8.6

Radioactivity

The binding-energy curve shows that nuclear stability begins to decline once the atomic number exceeds ; nuclei beyond this point, together with certain lighter isotopes, are collectively called unsta…

8.6.1

Alpha decay

In alpha decay, an unstable nucleus emits an alpha particle - a nucleus, i.e. two protons and two neutrons bound together.

8.6.2

Beta decay

In beta decay, a radioactive nucleus emits either an electron or a positron; both are collectively called beta particles, with the positron being the electron's antiparticle - identical mass, but oppo…

8.6.3

Gamma decay

In both alpha and beta decay, the resulting daughter nucleus is very often left in an excited energy state rather than settling directly into its true ground state; such excited nuclear states typical…

8.6.4

Law of radioactive decay

A real radioactive sample contains an enormous number of nuclei, and not all of them decay simultaneously - each individual nucleus decays at a random, unpredictable moment (like the toss of a coin),…

8.6.5

Half-life

It is generally very hard to say exactly when all of the nuclei in a sample will have decayed (since the decay law implies this technically takes infinite time), but it is straightforward to calculate…

8.6.6

Carbon dating

One of the most striking practical applications of beta decay is radiocarbon (carbon) dating, a technique for estimating the age of ancient organic material.

8.6.7

Discovery of Neutrons

In 1930, the German physicists Walther Bothe and Herbert Becker discovered that bombarding beryllium with alpha particles produced a highly penetrating, uncharged radiation, one able to pass through t…

8.7

Nuclear Fission

In 1939, the German scientists Otto Hahn and Fritz Strassmann discovered that when a uranium nucleus is bombarded with a neutron, it can break apart into two smaller nuclei of roughly comparable mass,…

8.8

Nuclear Fusion

Nuclear fusion is the process by which two or more light nuclei (typically each with mass number ) combine to form a single, heavier nucleus.

Elementary particles

Until roughly the 1960s, protons, neutrons and electrons were all believed to be truly fundamental "building blocks" of matter, with nothing smaller inside them.

Fundamental forces of nature

Nature is now understood to be governed by exactly four fundamental forces, each responsible for a different domain of physical phenomena:

Summary

- A device used to study the conduction of electricity through gases is known as a gas discharge tube.

Concept Map

The chapter's concept map ties every topic together under the single title "Atomic and Nuclear Physics," branching into two broad halves that mirror the unit's two main themes.

Evaluation

70 Q

This section is the textbook's own end-of-chapter evaluation set for the unit, covering all the material from the electric discharge through gases up to elementary particles and the fundamental forces…

+I Multiple Choice Questions15 questions
  1. Q1Suppose an alpha particle accelerated by a potential of $V$ volt is allowed to collide with a nucleus whose atomic number is $Z$, then the d…Free
  2. Q2In a hydrogen atom, the electron revolving in the fourth orbit has angular momentum equal to (a) $h$ (b) $\dfrac{h}{\pi}$ (c) $\dfrac{4h}{\p…Free
  3. Q3Atomic number of a hydrogen-like atom with ionization potential 122.4 V for $n=1$ is (a) 1 (b) 2 (c) 3 (d) 4Free
  4. Q4The ratio between the radii of the first three orbits of a hydrogen atom is (a) 1:2:3 (b) 2:4:6 (c) 1:4:9 (d) 1:3:5Preview
  5. Q5The charge of cathode rays is (a) positive (b) negative (c) neutral (d) not definedPreview
  6. Q6In J.J. Thomson's e/m experiment, a beam of electrons is replaced by that of muons (a particle with the same charge as an electron but mass…Preview
  7. Q7The ratio of the wavelengths for the transition from $n=2$ to $n=1$ in $\text{Li}^{++}$, $\text{He}^{+}$ and $H$ is (a) 1:2:3 (b) 1:4:9 (c)…Preview
  8. Q8The electric potential between a proton and an electron is given by $V=V_0\ln\!\left(\dfrac{r}{r_0}\right)$, where $r_0$ is a constant. Assu…Preview
  9. Q9If the nuclear radius of $^{27}\text{Al}$ is 3.6 fermi, the approximate nuclear radius of $^{64}\text{Cu}$ is (a) 2.4 F (b) 1.2 F (c) 4.8 F…Preview
  10. Q10The nucleus is approximately spherical in shape. Then the surface area of a nucleus having mass number $A$ varies as (a) $A^{2/3}$ (b) $A^{4…Preview
  11. Q11The mass of a $^{7}_{3}\text{Li}$ nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of…Preview
  12. Q12$M_p$ denotes the mass of a proton and $M_n$ denotes the mass of a neutron. A given nucleus of binding energy $B$ contains $Z$ protons and $…Preview
  13. Q13A radioactive nucleus (initial mass number $A$ and atomic number $Z$) emits 2 alpha particles and 2 positrons. The ratio of the number of ne…Preview
  14. Q14The half-life period of a radioactive element A is the same as the mean life time of another radioactive element B. Initially both have the…Preview
  15. Q15A system consists of $N_0$ nuclei at $t=0$. The number of nuclei remaining after half of a half-life (that is, at time $t=\tfrac{1}{2}T_{1/2…Preview
+II Short answer questions27 questions
  1. Q1What are cathode rays?Free
  2. Q2Write the properties of cathode rays.Free
  3. Q3Give the results of Rutherford's alpha scattering experiment.Free
  4. Q4Write down the postulates of the Bohr atom model.Preview
  5. Q5What is meant by excitation energy?Preview
  6. Q6Define ionization energy and ionization potential.Preview
  7. Q7Write down the drawbacks of the Bohr atom model.Preview
  8. Q8What is distance of closest approach?Preview
  9. Q9Define impact parameter.Preview
  10. Q10Write the general notation of the nucleus of an element X. What does each term denote?Preview
  11. Q11What is an isotope? Give an example.Preview
  12. Q12What is an isotone? Give an example.Preview
  13. Q13What is an isobar? Give an example.Preview
  14. Q14Define the atomic mass unit (u).Preview
  15. Q15Show that nuclear density is almost constant for nuclei with $Z>10$.Preview
  16. Q16What is mass defect?Preview
  17. Q17What is the binding energy of a nucleus? Give its expression.Preview
  18. Q18Calculate the energy equivalent of 1 atomic mass unit.Preview
  19. Q19Give the physical meaning of binding energy per nucleon.Preview
  20. Q20What is meant by radioactivity?Preview
  21. Q21Give the symbolic representation of alpha decay, beta decay and gamma decay.Preview
  22. Q22In alpha decay, why does the unstable nucleus emit a $^{4}_{2}\text{He}$ nucleus? Why does it not emit four separate nucleons?Preview
  23. Q23What is the mean life of a nucleus? Give the expression.Preview
  24. Q24What is the half-life of a nucleus? Give the expression.Preview
  25. Q25What is meant by activity or decay rate? Give its unit.Preview
  26. Q26Define the curie.Preview
  27. Q27What are the constituent particles of a neutron and a proton?Preview
+III Long answer questions17 questions
  1. Q1Explain the J.J. Thomson experiment to determine the specific charge of an electron.Free
  2. Q2Discuss Millikan's oil drop experiment to determine the charge of an electron.Free
  3. Q3Derive the energy expression for the hydrogen atom using the Bohr atom model.Free
  4. Q4Discuss the spectral series of the hydrogen atom.Preview
  5. Q5Explain the variation of average binding energy with mass number by a graph and discuss its features.Preview
  6. Q6Explain in detail the nuclear force.Preview
  7. Q7Discuss the alpha decay process with an example.Preview
  8. Q8Discuss the beta decay process with examples.Preview
  9. Q9Discuss the gamma decay process with an example.Preview
  10. Q10Obtain the law of radioactive decay.Preview
  11. Q11Discuss the properties of the neutrino and its role in beta decay.Preview
  12. Q12Explain the idea of carbon dating.Preview
  13. Q13Discuss the process of nuclear fission and its properties.Preview
  14. Q14Discuss the process of nuclear fusion and how energy is generated in stars.Preview
  15. Q15Describe the working of a nuclear reactor with a block diagram.Preview
  16. Q16Explain in detail the four fundamental forces.Preview
  17. Q17Briefly explain the elementary particles of nature.Preview
+Exercisesi11 questions
  1. 8.1Consider two hydrogen atoms $H_A$ and $H_B$ in the ground state. Assume that hydrogen atom $H_A$ is at rest and hydrogen atom $H_B$ is movin…Free
  2. 8.2In the Bohr atom model, the frequency of transitions is given by $v=Rc\left(\dfrac{1}{n^2}-\dfrac{1}{m^2}\right)$, where $n<m$. Consider the…Free
  3. 8.3(a) A hydrogen atom is excited by radiation of wavelength 97.5 nm. Find the principal quantum number of the excited state. (b) Show that the…Free
  4. 8.4Calculate the radius of the earth if the density of the earth is equal to the density of the nucleus. [mass of earth $=5.97\times10^{24}$ kg…Preview
  5. 8.5Calculate the mass defect and the binding energy per nucleon of the $^{108}_{47}\text{Ag}$ nucleus. [atomic mass of Ag $=107.905949$ u]Preview
  6. 8.6Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially the samples have equal numbers of nucle…Preview
  7. 8.7On your birthday, you measure the activity of a sample of $^{210}\text{Bi}$ which has a half-life of 5.01 days. The initial activity that yo…Preview
  8. 8.8Calculate the time required for 60% of a sample of radon to undergo decay. Given $T_{1/2}$ of radon $=3.8$ days.Preview
  9. 8.9Assuming that the energy released by the fission of a single $^{235}_{92}\text{U}$ nucleus is 200 MeV, calculate the number of fissions per…Preview
  10. 8.10Show that the mass of radium ($^{226}_{88}\text{Ra}$) with an activity of 1 curie is almost a gram. Given $T_{1/2}=1600$ years.Preview
  11. 8.11Charcoal pieces of a tree found at an archaeological site have a carbon-14 content that is only 17.5% that of an equivalent sample of carbon…Preview

Books for Reference

The chapter closes with a short reading list of six standard modern-physics textbooks that the authors recommend to students who wish to explore atomic and nuclear physics in greater depth than the NC…

ICT Corner

The chapter ends with an "ICT Corner" activity box directing students to a free online virtual-lab simulation of Millikan's oil drop experiment, hosted at the Amrita Vishwa Vidyapeetham virtual labs p…

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 57 questions57 questions
  1. Q1The mass defect of a certain nucleus is found to be 0.03 amu. Its binding energy is : (a) 27.93 eV (b) 27.93 keV (c) 27.93 MeV (d) 27.93 GeVPreview
  2. Q2The energy of electron in the first orbit of hydrogen atom is $-13.6$ eV. Its potential energy is : (a) 13.6 eV (b) 27.2 eV (c) $-27.2$ eV (…Preview
  3. Q3Arrange electron (e), proton (p) and deutron (d) in the increasing order of their specific charge : (a) e, p, d (b) d, p, e (c) p, e, d (d)…Preview
  4. Q4In a Bainbridge mass spectrometer positive rays of the same element produce different traces. The traces correspond to : (a) isotopes (b) is…Preview
  5. Q5In hydrogen atom, which of the following transitions produce a spectral line of maximum frequency ? (a) 6 → 2 (b) 2 → 1 (c) 4 → 3 (d) 5 → 2Preview
  6. Q6The radio-isotope used in agriculture is : (a) ${}_{15}P^{31}$ (b) ${}_{15}P^{32}$ (c) ${}_{11}Na^{23}$ (d) ${}_{11}Na^{24}$Preview
  7. Q7The nuclei ${}_{13}Al^{27}$ and ${}_{14}Si^{28}$ are examples of : (a) isotopes (b) isobars (c) isotones (d) isomersPreview
  8. Q8The Rydberg constant for Hydrogen is $1.097\times10^7$ m$^{-1}$. Calculate the short wavelength limit of Lyman series.Preview
  9. Q9Define curie.Preview
  10. Q10Write any three properties of neutrons.Preview
  11. Q11A reactor is developing energy at the rate of 32 MW. Calculate the required number of fissions per second of ${}_{92}U^{235}$. Assume that e…Preview
  12. Q12Explain the construction and working of a Geiger-Muller Counter.Preview
  13. Q13The explosion of atom bomb is based on the principle of : (a) fusion reaction (b) uncontrolled fission reaction (c) thermonuclear reaction (…Preview
  14. Q14The ionisation power is maximum for : (a) $\gamma$-rays (b) neutrons (c) $\beta$-particles (d) $\alpha$-particlesPreview
  15. Q15X-ray is : (a) conversion of energy into mass (b) phenomenon of conversion of kinetic energy into radiation (c) principle of conservation of…Preview
  16. Q16The energy of electron in the excited state of hydrogen atom is $-0.85$ eV. If 'h' is Planck's constant, the angular momentum of electron in…Preview
  17. Q17Anaemia can be diagnosed by : (a) ${}_{26}Fe^{59}$ (b) ${}_{15}P^{31}$ (c) ${}_{11}Na^{24}$ (d) ${}_{15}P^{32}$Preview
  18. Q18Initial mass of ${}_{84}Po^{218}$ is 1 gram. After what time 0.875 gram of it will be disintegrated ? ($T_{1/2}=3$ minutes) (a) 12 minutes (…Preview
  19. Q19Calculate the longest wavelength that can be analysed by a rock salt crystal of spacing $d = 2.82$ Å in the first order.Preview
  20. Q20Write any three properties of $\beta$-rays.Preview
  21. Q21What is meant by pair production and annihilation ?Preview
  22. Q22Explain the spectral series of hydrogen atom. (Diagram not necessary)Preview
  23. Q23Calculate the time required for 60% of a sample of radon to undergo decay. Given $T_{1/2}$ of radon $= 3.8$ days. **OR** Find the energy rel…Preview
  24. Q24Explain emission and absorption spectra. (Diagram not necessary)Preview
  25. Q25State the postulates of Bohr atom model. Obtain the expression for the radius of the $n^{th}$ orbit of an electron based on Bohr's theory.Preview
  26. Q26Two samples of radioactive substances have the same quantity. $\dfrac{1}{16}$th portion of A and $\dfrac{1}{256}$th portion of B remain unde…Preview
  27. Q27The distance of closest approach of an α-particle reaching a nucleus with momentum 'p' is $r_0$. When the α-particle travels towards the sam…Preview
  28. Q28When a hydrogen atom absorbs an energy of 10.2 eV, the change in its angular momentum is : (a) $4.14\times10^{-15}$ Js (b) $0.525\times10^{-…Preview
  29. Q29Define curie.Preview
  30. Q30State and obtain Bragg's Law.Preview
  31. Q31Half lives of two radioactive elements are 12 hrs and 16 hrs respectively. If at any instant, the ratio of the amounts of radioactive substa…Preview
  32. Q32(a) Explain the spectral series of hydrogen atom. (Diagram not necessary) **OR** (b) Explain the function of AM radio transmitter with neat…Preview
  33. Q33(a) Explain the construction and working of a Geiger-Muller Counter. **OR** (b) Explain the working of photo emissive cell. Write any two ap…Preview
  34. Q34In Bohr Atom Model when the principal quantum number (n) increases the velocity of electron : (a) increases and then decreases (b) increases…Preview
  35. Q35The nucleus is approximately spherical in shape. Then the surface area of nucleus having mass number A varies as : (a) $A^{5/3}$ (b) $A^{2/3…Preview
  36. Q36What are the uses of X-rays ?Preview
  37. Q37What are the properties of neutrino ?Preview
  38. Q38What are the important inferences from the average binding energy curve ?Preview
  39. Q39The electric potential of an electron is given by $V = V_0 \ln\left(\dfrac{r}{r_0}\right)$, where $r_0$ is a constant. If Bohr atom model is…Preview
  40. Q40Calculate the radius of $^{197}_{79}\text{Au}$ nucleus.Preview
  41. Q41For the 5$^{th}$ orbit of hydrogen atom, find the : (i) Angular momentum (ii) Velocity of the electron revolving in the 5$^{th}$ orbit of hy…Preview
  42. Q42(a) (i) How do we obtain characteristic X-ray spectra ? (ii) Calculate the cut-off wavelength and cut-off frequency of X-rays from an X-ray…Preview
  43. Q43In an hydrogen atom, the electron revolving in the second orbit, has angular momentum : (a) $\dfrac{4h}{\pi}$ (b) $h$ (c) $\dfrac{2h}{\pi}$…Preview
  44. Q44What is meant by activity or decay rate ? Give its unit.Preview
  45. Q45What are Fraunhofer lines ? How are they useful in the identification of elements present in the Sun ?Preview
  46. Q46Calculate the amount of energy released in joules when 1 kg of $^{235}_{92}U$ undergoes fission reaction.Preview
  47. Q47Atomic number of H - like atom with ionization potential 122.4 V for n = 1 is : (a) 3 (b) 4 (c) 2 (d) 1Preview
  48. Q48What are electromagnetic waves ?Preview
  49. Q49Discuss the Beta$^{+}$ ($\beta^{+}$) decay process with an example.Preview
  50. Q50A radioactive element has N$_0$ number of nuclei at t = 0. The number of nuclei remaining after half of a half-life (that is, at time $t = \…Preview
  51. Q51What is mass defect ? Give its expression.Preview
  52. Q52Find the (i) Angular momentum (ii) Velocity of the electron revolving in the 5$^{th}$ orbit of hydrogen atom of radius 13.25 Å.Preview
  53. Q53(a) Obtain the law of radioactive decay. **OR** (b) What is absorption spectrum ? Explain the types of absorption spectrum.Preview
  54. Q54The mass of a $^{7}_{3}\text{Li}$ nucleus is 0.042 u less than the sum of the masses of all its nucleons. The average binding energy per nuc…Preview
  55. Q55Write the properties of cathode rays. (any two)Preview
  56. Q56Show that nuclear density is almost constant for nuclei with Z >10.Preview
  57. Q57(i) What is binding energy of a nucleus ? Write its expression. (ii) Compute the binding energy of $^{4}_{2}\text{He}$ nucleus using the fol…Preview