UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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

Discuss the significance of Gellmann-Nishijima relation in strange particle production and decay. Give examples in support of your answer. Obtain quark quantum numbers using the modified relation for quarks.

Illustrate with any five examples that production of strange particles conserves strangeness, parity and isotopic spin while their decay violates all these quantities.

Describe important experimental facts that led Pauli to postulate the existence of neutrino particle.

(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) 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) 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) 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) 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) 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?

(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}.

• Show that the spin states of electron are orthogonal to each other.
• State the spin angular momentum commutation relations.
• Give the explicit forms of all the Pauli spin matrices.

(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) 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.

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.

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

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.

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

A conducting sphere of radius `a' is placed in a uniform electric field E_0. Using the method of images, show that the potential function is given by \phi = -E_0 \left(r - \frac{a^3}{r^2}\right) \cos \theta.

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