Core X : Nuclear and Particle Physics

Similar : CBCS 2019: DSE 2 (Nuclear and Particle Physics) AND Old Core-IX (Elements of Modern Physics).

(atoms in electric and magnetic field, Nuclear physics, nuclear models and nuclear reactions, particle physics.)

Syllabus

Unit I

Atoms in Electric and Magnetic Fields: Electron angular momentum. Space quantization, Electron Spin and Spin Angular Momentum, Larmor's Theorem, Spin Magnetic Moment, Stern Gerlach Experiment, Vector Atom Model, L-S and J-J coupling, Zeeman Effect, Electron Magnetic Moment and Magnetic Energy, Gyro magnetic Ratio and Bohr Magnetron. Atoms in External Magnetic Fields: Normal and Anomalous Zeeman Effect, Paschen back and Stark-Effect (qualitative Discussion only).

Unit II

Nuclear Physics- : Nuclear composition, charge, size, shape, mass and density of the nucleus; Nuclear angular momentum; Nuclear magnetic dipole moment ; Electric quadrupole moment; Mass defect; Packing fraction and Binding energy; Stability of nuclei (N vs Z curve), Binding energy curve. semi-empirical mass formula; Nuclear Forces: General concept of nuclear force; Yukawa Meson field theory of nuclear forces; Properties of Nuclear forces. Radioactive disintegration; Properties of alpha, beta, gamma rays; law of radioactive decay; successive radioactive decay; radioactive equilibrium; Radioisotopes; application of radioactivity (Agriculture, Medicinal, Industrial and Archaeological).

Unit III

Nuclear models: Liquid Drop model; Shell model; magic number in the nucleus; Alpha decay: Alpha particles spectra; Gamow's theory of Alpha decay; Beta decay: Shape of Beta ray spectrum; Explanation of Beta decay on the basis of Neutrino and Antineutrino hypothesis; Fermi theory of Beta decay; Selection rules; Gamma ray emission,
Nuclear reactions: Kinds of Nuclear reactions; Nuclear reaction kinematics; Q-value; Compound Nucleus and concept of direct reactions; Conservation laws; Nuclear reaction cross-sections. Nuclear energy: Nuclear Fission; Chain reaction and Critical Mass; Nuclear Reactors and it's basic components; Nuclear Fusion; Condition for the maintained Fusion reactions; Energy production in stars; Fusion reaction in Sun, Principle of atomic bomb and hydrogen bomb.

Unit IV

Particle Physics Classification of particles-antiparticles and their interactions; Conservation laws; Charges; Isospin; Baryon number; Lepton number; Strangeness; Hyper charge; Parity; Charge conjugation; CPT theorem; Conservation laws; Quark as the building blocks of Hadrons; Quark Model; Colour degree of freedom, Symmetry Classification of elementary particles; Higgs Boson Particle (God particle), elementary idea on Large Hadron collider (LHC), The future of universe, Dark matter and dark energy.

Text Books

Concepts of Modern Physics Arthur Beiser (McGrawHill)
Modern Physics Murugeshan and Sivaprasad (S.Chand)
Cohen B. L., "Concepts of Nuclear Physics", McGraw Hill Education.
Tayal D. C., "Nuclear Physics", Himalaya Publishing House.
Patel S. B., "Nuclear Physics: An Introduction", New Age International Publishers.
Singh Jahan, "Fundamental of Nuclear Physics", Pragati Publications

Reference Books

Quantum Mechanics: Theory and Applications, A. K. Ghatak and S. Lokanathan, (Macmillan)
Introduction to Quantum Theory, David Park (Dover Publications)
Theory and Problems of Modern Physics, Schaum's outline, R. Gautreau and W. Savin (Tata McGraw-Hill)
Modern Physics - Serway (CENGAGE Learnings)
Physics of Atoms and Molecules - Bransden and Joachim (Pearson India)
Atomic and Nuclear Physics - A. B. Gupta (New Central)
Theoretical Nuclear Physics, J. M. Blatt and V. F. Weisskopf (Springer)

Questions

2025 | +3-V-S-CBCS(MS)-Sc(H)-DSE-II-Phy | Full Marks: 80

PART-I | Answer all Questions. | 1x12

Nuclear density is in the order of ____ kg/m³.
The nuclear force between nucleons is due to the exchange of ______.
Neutrino hypothesis is given to explain _.
The nuclei with __ number of protons and ___ number of neutrons are most stable.
For A≥ 30, the average binding energy of a nucleus is in the order of _____.
The variation of pairing energy of a nucleus with mass number A is given by ______.
The ground state of any even-even nucleus has spin and parity ______.
The time during which the Geiger Muller counter does not record pulses is called ______.
Scintillation counters are highly suitable for ______.
The cyclotron frequency of a particle in a magnetic field is independent of _____ of particle.
Spin of gluon is _____.
Baryon can have spin _____ .

PART-II | Answer any eight within two to three sentences | 2x8

Calculate the binding energy in MeV of $_2 He^4$ . Where mass of $_2 He^4 = 4.003875$ amu; mass of proton = 1.008145 amu and mass of neutron = 1.008986 amu.
Explain pair production process.
Explain why a stable system of two neutrons has not been observed.
Write semi-empirical mass formula.
The nuclear radius of $8 O^{16}$ is $3 \times 10^{-15}$ meters. Find the nuclear radius of ${26} Fe^{54}$.
Write the principle of neutron detector.
Why cannot we detect $\beta-$ and $\gamma-$ particles by an ionization chamber?
Write the disadvantages of a linear accelerator.
What do you mean by charge conjugation ?
What is the $J/\Psi$ particle?

PART-III | Answer any eight of the following (in maximum 75 words.) | 3x8

Explain neutrino hypothesis of $\beta-$decay.
Justify that the nucleus contains only protons and neutrons.
What are magic nuclei ? Give suitable examples.
Predict spin and parity of $_9 F^{17}$.
Why does the plateau of the G-M tube have a nonzero slope ?
What factors are required for the selection of carrier gas in a gas-filled counter
How does the Cyclotron accelerator operate ?
What is CP violation in particle physics?
Discuss about leptons.
Determine whether following reaction is allowed or forbidden. $$ \pi^- + n \rightarrow \lambda^0 + K^+$$

PART-IV | Answer within 500 words each. | 7x4

Discuss the following nuclear properties:
a. Angular moment
b. Magnetic moment
c. Electric moment.
OR
What is a-decay? Discuss Gamow's theory of $\alpha-$decay.
Discuss similarities and differences between nucleus and liquid drop. Also write its successes and failures.
OR
Give salient feature of shell model and point out its successes and failures.
Discuss the construction, principle, working and properties of an ionisation chamber.
OR
Discuss the principle and working of photomultiplier tubes.
Discuss about four fundamental interactions.
OR
What are quarks? Describe the quark model.

2025 | +3-IV-S-CBCS(MS)-Sc(H)-Core-IX-Phy-R&B | Full Mark 60

PART-I | Answer all the questions | 1x8

At stopping potential the photo current becomes _____.
Rayleigh-Jeans law is correct only in the _____ wavelength region.
In Rutherford atom model, classical theory shows that the electron would reach the nucleus in time T = _____.
If a wave packet is described by $\phi(x) = Ae^{-x^2}/(2\sigma^2)$, then the momentum uncertainity is proportional to ____.
Coulomb energy of $^{73}_{32}Ge$ is ______.
The half-life of $^{198} Au$ 2.70 days. The decay constant of $^{198} Au$ is ______.
The nuclear force _____ range.
The energy necessary to remove a proton or a neutror from a nucleus is typically about ____MeV.

PART-II | Answer any eight within two to three sentences | 1.5 ×8

Calculate the ionisation potential of He-atom in the ground a state.
Discuss the draw backs of Rutherford's atomic model.
Calculate the de Broglie wavelength of a neutron of energy 1 MeV.
Justify that the de Broglie wavelength associated only with subatomic particles is observable.
Determine the stable nucleus that has a radius 1/3 that of $^{189}O$s.
Derive the decay law $N= N_0 e^{-\lambda t}$.
What is the difference between the binding energies of $^3_2He$ and $^3_1H$.
What is the velocity of the electron in the ground state of Bohr's hydrogen atom in terms of speed of light ?
$^{23}Ne$ decays to $^2Na$ by negative beta emission. What is the maximum kinetic energy of the emitted electron ?
Find the total binding energy B and also the average binding energy per nucleon B/A for $^{56}_{26}Fe$.

PART-III | Answer any eight of the following in maximum 75 words. | 2× 8

Certain ocean waves travel with a phase velocity $v_{phase}=\sqrt{g\lambda /2\pi}$ where g is the acceleration due to gravity. What is the group velocity of a wave packet of these waves ?
Show that the Compton shift of the scattered radiation varies from 0 to 0.484 $^°A$ if the angle of scattering varies from 0 to 180°.
An electron and a proton have the same de Broglie wavelength. Prove that the energy of the electron is greater.
To what accuracy the mass of the meson with life-time of $10^{-23}s$ can be determined ?
Show that $^{236}_{94}Pu$ is unstable and will $\alpha$-decay.
Find the kinetic energy of the $\alpha$-particle emitted in the $\alpha$-decay process of $^{236}Ra$.
Complete the following decays: (i) $^{27}{14}Si{13} \rightarrow ^{27}{13}Al{14} + $ _ (ii) $^{238}{92}U{136} \rightarrow \alpha + $ __
State and explain Bohr's correspondence principle.
The amount of energy required to ionise hydrogen atom in its ground state is 13.58 eV. How much energy is needed to excite it from the ground state to n=4 level ?
The lifetime of an excited state of an atom is $10^{-8}$ sec. Calculate the minimum uncertainty in the determination of energy of the excited state.

PART-IV | Answer within 500 words each. | 6×4

According to Bohr's theory, how many revolutions will an electron make in the first excited state of hydrogen if the life time of that state is $10^{-8}$s ?
OR
Ionisation energy of hydrogen atom is 13.6 eV. Calculate the wavelength of the first time of Balmer series.
State Heisenberg's uncertainity relation. Use uncertainity principle to show that electron can not be a constituent of the nucleus.
OR
By doing a nuclear diffraction experiment, you measure the de Broglie wave length of a proton to be 9.16 fm.
a. What is the speed of the proton ?
b. hrough what potential differential must be accelerated to achieve that speed.
Using the liquid drop model, find the most stable isobar for a given odd A. For A=43, 77 find the most stable nucleus.
OR
Use the semiempirical mass formula to calculate the binding energy of $^{40}_{20}Ca$. What is the percentage of discrepancy between the value and the actual value ?
In terms of parent and daughter restmass, determine Q-values for $\beta^-$ decay, $\beta^+$ decay and electron capture.
OR
Compute the Q-value for the $^{28}U \, \rightarrow ^{206}Pb$ decay chain and find the rate of energy production per gram of uranium.

2022 | +3-IV-S-CBCS(MS)-SC(H)-Core-IX-Phy | Full Marks : 60

PART-I | Answer all the questions

The phenomenon of emission of electrons from metallic surfae when light falls on it is called _____.
According to Bohr's atomic model, the angular momentum of electron in a given orbit is integral multiple of _____.
For _____ medium group velocity and phase velocity are equal.
De-Broglie hypothesis is expressed as _____.
The semi-empirical mass formula is based on _____ model .
Nuclear radius varies with mass number 'A' as _____.
$\beta-$decay is a consequence of _____ force.
Antiparticle of electron is _____.

PART-II | Answer any eight within two to three sentences | 1.5x8

What does the Franck-Hertz experiment prove ?
Find the ratio of radius of 4th Bohr's orbit to 7th Bohr's orbit.
Explain wave-particle duality.
Find de-Broglie wavelength of an electron which has been accelerated from rest through a potential difference of 100 V.
What is wave packet ?
What is nuclear force ?
Define packing fraction and draw the graph of packing fraction versus mass number.
Define isobar and isotope with examples.
State law of radioactivity decay.
What is pair creation process ?

PART-III | Answer in 75 words | 2×8

Discuss briefly Sommerfeld's atomic model.
Discuss briefly Compton effect.
When light of wavelength 2200 $\AA$ falls on Cu surface, photo electron are emitted. Determine the maximum kinetic energy of the photo electrons. The work function of Cu is 4.65 eV.
Show that uncertainty principle rules out the possibility of electron being inside the nucleus.
Distinguish between phase velocity and group velocity.
Draw the graph showing the variation of binding energy per nucleon with mass number. Write two inferences drawn from the graph.
Find energy equivalent of 1 amu in Mev.
State limitations of liquid-drop model.
Distinguish between nuclear fission and fusion.
The decay constant of a substance is 0.84 $s^{-1}$. Find the half-life and mean-life of the substance.

PART-IV | Answer within 500 words each. | 6x4

4) Stating various assumptions used in Rutherford's scattering experiment, derive Rutherford's scattering formula.
OR
Stating Bohr's postulates, derive an expression for the freauencies of radiation emitted from hydrogen atom. Hence explain the various spectral series.

5) Discuss in detail the Davisson and Germer experiment. Explain how the experimental results directly confirm the de-Broglie hypothesis of matter wave.
OR
State Heisenberg uncertainty principle. Show how gamma- ray microscope thought experiment illustrates the principle Also find ground state energy of harmonic oscillator using the principle.

6) Discuss semi-empirical mass formula explaining each term in expression.
OR
Discuss about the nuclear shell model.

7) Describe salient features of $\beta-$decay. Explain Pauli's hypothesis of neutrino for $\beta-$decay. Mention properties of neutrino too.
OR
What is $\alpha-$decay? Discuss Gamow's theory of $\alpha-$decay.

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