PYQ Bank

Classify the Indian power reactors into BWR, PHWR and FBR varieties, explaining the acronyms, type of fuel used and location for each variety.

A nuclear reactor operates at a power level of 10^8\text{ W}. What will be the flux of neutrons required to maintain this power level ? Given that a free neutron has an average lifetime of 10^{-3}\text{ second} before its capture in a uranium nucleus and energy released per fission is 200\text{ MeV}.

Use conservation laws to find the nature of residual nucleus when 50.0\text{ MeV} proton beam strikes the beryllium (^{9}_{4}\text{Be}) target nucleus producing a beam of neutrons.

Describe briefly the various cycles for energy production in stars, relating them to the life history of a star. "Fusion reactors operate in the core of stars but have not become a reality on earth as yet." Comment on the statement.

(i) What is Raman effect ? How does it differ from Rayleigh scattering? Write down its important applications. (ii) Explain Raman effect with the aid of quantum mechanical theory. (iii) Why is Raman effect considered complimentary to infrared absorption spectra? (iv) A Raman Stokes' line is observed at 552\text{ nm} when a sample is excited by Hg green line of wavelength 546\text{ nm}. Calculate the wavelength of anti-Stokes' line.

(i) On the basis of vector atom model, discuss briefly the L-S and J-J coupling schemes. (ii) Write down expressions for spin angular momentum, orbital angular momentum and total angular momentum under L-S coupling scheme. (iii) Obtain the energy states for ^{2}\text{He} atom for n = 1, 2, 3 levels (n is principal quantum number). Draw the energy level diagram. Does L-S coupling scheme hold good in ^{80}\text{Hg} atom which like He has 2 optical electrons (6S^2) ? Comment.

(i) What is Lamb shift? Explain it by illustrating through a suitable energy level diagram. Has Lamb shift been observed in any atom other than hydrogen? (ii) How does the 21 cm hydrogen line originate? Comment on its astronomical applications.

(i) Discuss qualitatively the occurrence of rotational energy levels at a diatomic molecule. Write down the selection rule. (ii) Is it possible to obtain rotational spectra of \text{H}_2, \text{HF}, \text{O}_2, and \text{NO} molecules? Can one obtain pure rotational spectra in emission? Comment (on both of the above-mentioned queries). (iii) In \text{CO} molecule J = 0 \rightarrow J = 1 line occurs at frequency 1.153 \times 10^{11}\text{ Hz}. Calculate the moment of inertia of \text{CO} molecule.

(i) State and explain Franck-Condon principle. (ii) In three separate pairs of electronic states (one ground and another upper state) of diatomic molecules, the average internuclear distances are : (1) equal, (2) slightly greater, and (3) appreciably greater. In accordance with Franck-Condon principle, obtain most favourable transitions from the ground state vibrational levels to the upper state vibrational levels in each of the three situations. Illustrate the transitions in all the aforesaid situations by drawing suitable energy level diagrams.

(i) Write down the matrix representation of the energy operator of a linear oscillator. (ii) A linear oscillator is prepared in the state given by \psi(x) = 1/\sqrt{5} \{\hat{\psi}_0(x) + \sqrt{2} \hat{\psi}_1(x) + \sqrt{2} \hat{\psi}_2(x)\} Evaluate the energy of the oscillator in this state.

(i) Quantum theoretical methods have established themselves to explain natural phenomena in contemporary Physics. Comment. (ii) Formulate the axioms of quantum theory. (iii) State Born's condition on a wave function. What is its physical meaning?

A particle is in a quantum system with a parabolic potential well. (i) Using appropriate method find the ground state energy. (ii) Obtain an expression for the ground state.

(i) Find the eigenstates of the angular momentum vector component L_z of a spherically symmetric system. (ii) Write down any two properties of the Pauli matrices after defining through an expression.

(i) Give briefly an account on the important historical developments to establish the concept of electron spin. (ii) Write down the eigenvalue and spin state of an electron for the spin operator \hat{S}. (i) Show that the spin states of electron are orthogonal to each other. (ii) State the spin angular momentum commutation relations. (iii) Give the explicit forms of all the Pauli spin matrices.

Derive an expression for the Maxwellian distribution of velocities for the molecules of an ideal gas.

Calculate the increase in entropy when 1 kg ice melts at zero degree centigrade. The Latent heat of fusion of ice is 3.36 \times 10^5\text{ joules/kg}. (Assume that the melting is an isothermal reversible process)

Obtain van der waals' equation of state for real gases. What is the value of critical coefficient for an ideal gas ? Show that the value of the critical coefficient for van der Waals' gas is independent of the type of gas.

How can one obtain a temperature and identify the elements in stellar bodies using Saha's thermal ionisation equation ?

From Planck's radiation law, derive Wien's displacement law and Rayleigh Jean's law.

Calculate the electric field as a function of position due to a dipole whose potential is given by V = \frac{P \cos \theta}{4 \pi \epsilon_0 r^2} \quad \text{where } r = \sqrt{x^2 + y^2} The dipole is located at the origin of the x, y axis system.