UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Considering atoms hard, uniform spheres, find the number of atoms per unit cell and packing fraction for simple cubic, bcc and fcc structures.

The wavelength of a prominent X-ray line from a copper target is 0.1512\,\mathrm{nm}. The radiation, when diffracted with (111) plane of a crystal with fcc structure, corresponded to a Bragg angle of 20.2^\circ. If the density of the crystal is 2698\,\mathrm{kg/m^3} and atomic weight is 26.98\,\mathrm{kg/kmol}, calculate the Avogadro number.

Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band edge at low temperature (assuming E_v=0).

Explain why each of the following particles cannot exist according to the quark model.

(i) A Baryon of spin 1

(ii) An anti-Baryon of electric charge +2

Which of the following decays are allowed and which are forbidden? If the decay is allowed, state which interaction is responsible. If it is forbidden, state which conservation law its occurrence would violate.

(i) n\to p+e^{-}+\bar{\nu}_e

(ii) \Lambda^{0}\to\pi^{+}+\pi^{-}

(iii) \pi^{-}\to e^{-}

(iv) \pi^{0}\to e^{-}e^{+}+\nu_e+\bar{\nu}_e

(v) \pi^{+}\to e^{+}e^{-}+\mu^{+}+\nu

Write down the Weizsäcker semi-empirical mass formula and explain each term. Explain why {}^{238}_{92}\mathrm{U} nuclide is an \alpha-emitter and not a \beta^--emitter?

Show that for a specific value (n,l), there exists a large degeneracy relative to the energy characterized by the quantum number (N). Find the shell closures and the magic numbers predicted by harmonic oscillator potential.

A neutron and a proton can undergo radiative capture at rest: n+p \longrightarrow d+\gamma Find the energy of the photon emitted in this capture. Is the recoil of the deuteron important?

If the nuclear force is charge independent and a neutron and proton form a bound state then why is there no bound state for two neutrons? What information does this provide on the nucleon-nucleon force?

(i) In a diatomic molecule when one constituent atom is replaced by one of its heavier isotopes, what change takes place in the rotational spectrum?

(ii) Calculate the change in rotational constant B when hydrogen is replaced by deuterium in the hydrogen molecule.

(iii) Draw the spectra of rigid and non-rigid rotors by using the schematic representation of the rotational energy levels and comment on it.

Show that the Landé g-factor for pure orbital angular momentum and pure spin angular momentum are 1 and 2 respectively. Further, evaluate the g-factor for the state {}^3P_1.

An atomic state is denoted by {}^4D_{5/2}. Find the values of L, S and J. For this state, what should be the minimum number of electrons involved? Suggest a possible electronic configuration.

(i) Why does Stern-Gerlach experiment enjoy so much importance in atomic physics?

(ii) Draw the schematic diagram of this experiment and comment on the shapes of the magnet pole pieces.

(iii) Why was the atomic beam of silver used in this experiment?

Calculate the magnetic field strength required to observe the NMR spectrum of protons in benzene at 120\,\mathrm{MHz}. [Given the value of nuclear g-factor g_N for protons is 5.585]

Define Franck-Condon principle. How does it help in explaining the intensity distribution of vibrational-electronic spectra of diatomic molecules.

(i) Briefly explain the effect of anharmonicity on the vibrational spectra of diatomic molecules.

(ii) Calculate the average period of rotation of HCl molecule if it is in the J=3 state. The internuclear distance and the moment of inertia of HCl are 0.1274\,\mathrm{nm} and 0.0264\times10^{-45}\,\mathrm{kg\,m^2} respectively.

Show that E_n=\langle V\rangle in the stationary states of the hydrogen atom.

Obtain the normalized eigenvectors of \sigma_x and \sigma_y matrices.

What is de Broglie concept of matter wave? Evaluate de Broglie wavelength of Helium that is accelerated through 300\mathrm{V}. (Given mass of proton = mass of neutron = 1.67\times10^{-27}\,kg)

The raising (J_+) and lowering (J_-) operators are defined by J_+=J_x+iJ_y and J_-=J_x-iJ_y respectively. Prove the following identities:

(i) [J_z,J_\pm]=\pm\hbar J_\pm

(ii) J_-J_+=J^2-J_z^2-\hbar J_z