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…
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Bohr Model Energy Levels
Imagine you're rolling a marble on a staircase. The marble can rest on any step — step 1, step 2, step 3 — but it can never float halfway between two steps. The staircase forces the marble into specific, fixed positions.
Most relevant Q&A
- Consider 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
- Atomic number of a hydrogen-like atom with ionization potential 122.4 V for $n=1$ is (a) 1 (b) 2 (c) 3 (d) 4Free
- Derive the energy expression for the hydrogen atom using the Bohr atom model.Free
- The 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
- What is meant by excitation energy?Preview
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Introduction
Everything around us that occupies space is matter, and matter appears in the forms solid, liquid and gas.
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.
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.
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.
Atom Models
Around 400 BC, the Greek philosophers Leucippus and Democritus first proposed that matter, if repeatedly subdivided, would eventually yield indivisible atoms.
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…
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…
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,…
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…
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:
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.
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…
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…
Isotopes, isobars, and isotones
Nuclei can be classified and compared along three different axes, depending on which of , or they share:
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).
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…
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…
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…
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.
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…
Alpha decay
In alpha decay, an unstable nucleus emits an alpha particle - a nucleus, i.e. two protons and two neutrons bound together.
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…
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…
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),…
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…
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.
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…
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,…
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 QThis 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
- 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
- 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
- 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
- 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
- Q5The charge of cathode rays is (a) positive (b) negative (c) neutral (d) not definedPreview
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Q1What are cathode rays?Free
- Q2Write the properties of cathode rays.Free
- Q3Give the results of Rutherford's alpha scattering experiment.Free
- Q4Write down the postulates of the Bohr atom model.Preview
- Q5What is meant by excitation energy?Preview
- Q6Define ionization energy and ionization potential.Preview
- Q7Write down the drawbacks of the Bohr atom model.Preview
- Q8What is distance of closest approach?Preview
- Q9Define impact parameter.Preview
- Q10Write the general notation of the nucleus of an element X. What does each term denote?Preview
- Q11What is an isotope? Give an example.Preview
- Q12What is an isotone? Give an example.Preview
- Q13What is an isobar? Give an example.Preview
- Q14Define the atomic mass unit (u).Preview
- Q15Show that nuclear density is almost constant for nuclei with $Z>10$.Preview
- Q16What is mass defect?Preview
- Q17What is the binding energy of a nucleus? Give its expression.Preview
- Q18Calculate the energy equivalent of 1 atomic mass unit.Preview
- Q19Give the physical meaning of binding energy per nucleon.Preview
- Q20What is meant by radioactivity?Preview
- Q21Give the symbolic representation of alpha decay, beta decay and gamma decay.Preview
- Q22In alpha decay, why does the unstable nucleus emit a $^{4}_{2}\text{He}$ nucleus? Why does it not emit four separate nucleons?Preview
- Q23What is the mean life of a nucleus? Give the expression.Preview
- Q24What is the half-life of a nucleus? Give the expression.Preview
- Q25What is meant by activity or decay rate? Give its unit.Preview
- Q26Define the curie.Preview
- Q27What are the constituent particles of a neutron and a proton?Preview
+−III Long answer questions17 questions
- Q1Explain the J.J. Thomson experiment to determine the specific charge of an electron.Free
- Q2Discuss Millikan's oil drop experiment to determine the charge of an electron.Free
- Q3Derive the energy expression for the hydrogen atom using the Bohr atom model.Free
- Q4Discuss the spectral series of the hydrogen atom.Preview
- Q5Explain the variation of average binding energy with mass number by a graph and discuss its features.Preview
- Q6Explain in detail the nuclear force.Preview
- Q7Discuss the alpha decay process with an example.Preview
- Q8Discuss the beta decay process with examples.Preview
- Q9Discuss the gamma decay process with an example.Preview
- Q10Obtain the law of radioactive decay.Preview
- Q11Discuss the properties of the neutrino and its role in beta decay.Preview
- Q12Explain the idea of carbon dating.Preview
- Q13Discuss the process of nuclear fission and its properties.Preview
- Q14Discuss the process of nuclear fusion and how energy is generated in stars.Preview
- Q15Describe the working of a nuclear reactor with a block diagram.Preview
- Q16Explain in detail the four fundamental forces.Preview
- Q17Briefly explain the elementary particles of nature.Preview
+−Exercisesi11 questions
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 8.8Calculate the time required for 60% of a sample of radon to undergo decay. Given $T_{1/2}$ of radon $=3.8$ days.Preview
- 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
- 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
- 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 questionsHide questions57 questions
- 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
- 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
- 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
- Q4In a Bainbridge mass spectrometer positive rays of the same element produce different traces. The traces correspond to : (a) isotopes (b) is…Preview
- 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
- Q6The radio-isotope used in agriculture is : (a) ${}_{15}P^{31}$ (b) ${}_{15}P^{32}$ (c) ${}_{11}Na^{23}$ (d) ${}_{11}Na^{24}$Preview
- Q7The nuclei ${}_{13}Al^{27}$ and ${}_{14}Si^{28}$ are examples of : (a) isotopes (b) isobars (c) isotones (d) isomersPreview
- Q8The Rydberg constant for Hydrogen is $1.097\times10^7$ m$^{-1}$. Calculate the short wavelength limit of Lyman series.Preview
- Q9Define curie.Preview
- Q10Write any three properties of neutrons.Preview
- 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
- Q12Explain the construction and working of a Geiger-Muller Counter.Preview
- Q13The explosion of atom bomb is based on the principle of : (a) fusion reaction (b) uncontrolled fission reaction (c) thermonuclear reaction (…Preview
- Q14The ionisation power is maximum for : (a) $\gamma$-rays (b) neutrons (c) $\beta$-particles (d) $\alpha$-particlesPreview
- Q15X-ray is : (a) conversion of energy into mass (b) phenomenon of conversion of kinetic energy into radiation (c) principle of conservation of…Preview
- 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
- Q17Anaemia can be diagnosed by : (a) ${}_{26}Fe^{59}$ (b) ${}_{15}P^{31}$ (c) ${}_{11}Na^{24}$ (d) ${}_{15}P^{32}$Preview
- 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
- Q19Calculate the longest wavelength that can be analysed by a rock salt crystal of spacing $d = 2.82$ Å in the first order.Preview
- Q20Write any three properties of $\beta$-rays.Preview
- Q21What is meant by pair production and annihilation ?Preview
- Q22Explain the spectral series of hydrogen atom. (Diagram not necessary)Preview
- 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
- Q24Explain emission and absorption spectra. (Diagram not necessary)Preview
- 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
- 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
- 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
- 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
- Q29Define curie.Preview
- Q30State and obtain Bragg's Law.Preview
- 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
- Q32(a) Explain the spectral series of hydrogen atom. (Diagram not necessary) **OR** (b) Explain the function of AM radio transmitter with neat…Preview
- 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
- Q34In Bohr Atom Model when the principal quantum number (n) increases the velocity of electron : (a) increases and then decreases (b) increases…Preview
- 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
- Q36What are the uses of X-rays ?Preview
- Q37What are the properties of neutrino ?Preview
- Q38What are the important inferences from the average binding energy curve ?Preview
- 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
- Q40Calculate the radius of $^{197}_{79}\text{Au}$ nucleus.Preview
- 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
- 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
- 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
- Q44What is meant by activity or decay rate ? Give its unit.Preview
- Q45What are Fraunhofer lines ? How are they useful in the identification of elements present in the Sun ?Preview
- Q46Calculate the amount of energy released in joules when 1 kg of $^{235}_{92}U$ undergoes fission reaction.Preview
- Q47Atomic number of H - like atom with ionization potential 122.4 V for n = 1 is : (a) 3 (b) 4 (c) 2 (d) 1Preview
- Q48What are electromagnetic waves ?Preview
- Q49Discuss the Beta$^{+}$ ($\beta^{+}$) decay process with an example.Preview
- 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 $t = \…Preview
- Q51What is mass defect ? Give its expression.Preview
- Q52Find the (i) Angular momentum (ii) Velocity of the electron revolving in the 5$^{th}$ orbit of hydrogen atom of radius 13.25 Å.Preview
- Q53(a) Obtain the law of radioactive decay. **OR** (b) What is absorption spectrum ? Explain the types of absorption spectrum.Preview
- 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
- Q55Write the properties of cathode rays. (any two)Preview
- Q56Show that nuclear density is almost constant for nuclei with Z >10.Preview
- 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