UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Calculate in terms of the nuclear magneton, \mu_{\mathrm{N}}, the magnetic dipole moment of {}^{3}S_{1} state of deuteron. Given, \mu_{\mathrm{p}}=2\cdot792847\mu_{\mathrm{N}} and \mu_{\mathrm{n}}=-1.913042\mu_{\mathrm{N}}.

Write down the Weizsäcker mass formula for the nuclear binding energy. Give short justification for each term of the formula.

Discuss in brief any two basic nuclear properties. Find the nuclear radius of {}^{12}_{6}\text{C} nucleus. Compare the atomic radius of carbon C-12 to the nuclear radius assuming the atomic radius to be 0\cdot 529 \times 10^{-10}\text{ m}. (R_0 = 1\cdot 2\text{ fm}) What inference will you get from the comparison with regards to nuclear size of carbon ?

The calcium line of wavelength \lambda = 4226\cdot 73\text{ \AA} (\text{P} \rightarrow \text{S}) exhibits normal Zeeman splitting when placed in a uniform magnetic field of 4\text{ Weber/metre}^3. Calculate the wavelength of three components of normal Zeeman pattern and the separation between them.

Explain how the magnetic moments of atoms, the space quantization of angular momentum and the spin of electron are measured using Stern–Gerlach experiment.

Calculate the frequency of the first Bohr orbit of hydrogen atom.

The potential energy of a diatomic molecule in terms of the interatomic spacing R is given by U(R)=-\frac{A}{R^2}+\frac{B}{R^{10}} where A=1.44\times10^{-3}\,\mathrm{J\,m^2} and B=2.19\times10^{-115}\,\mathrm{J\,m^{10}}. Calculate the equilibrium spacing, R_e and the dissociation energy.

Write the principle of nuclear magnetic resonance (NMR). Explain the design and working of NMR, and write its important applications.

Explain the mechanism of Fluorescent emission of radiation. Distinguish between Fluorescence spectra and Raman spectra of a diatomic molecule.

Determine the normal Zeeman splitting of the cadmium red line of 6438\,\mathring{\mathrm{A}}, when the atoms are places in a magnetic field of 0.009\,\mathrm{T}.

A Raman line associated with a vibrational mode which is both Raman and infrared active is found at 4600\text{ \AA} when excited by light of wavelength 4358\text{ \AA}. Calculate the wavelength of the corresponding infrared band.

Obtain an expression for the rotational energy levels of a diatomic molecule, taking it as a rigid rotator. Discuss its spectrum and the selection rule.

Explain the principle and working of Stern-Gerlach Experiment.

(i) Discuss about the validity criterion for the WKB approximation. (ii) Qualitatively explain alpha (\alpha) particle emission by WKB approximation.

(i) Draw a neat sketch of a finite rectangular potential barrier well of height U' and width L' that contains a particle whose energy E' is less than U'. Solve the Schrödinger equations of the particles outside the well. (ii) Plot wave functions and probability densities |\psi|^2 of the particle for the first three states. Compare the results with that of a particle in a box of infinite potential (U = \infty).

(i) What do you mean by expectation value of a physical quantity ? How does it help to extract information from a wave function ? (ii) A particle limited to move along x-axis has the wave function \psi = ax between x = 0 and x = 1, \psi = 0 elsewhere. Find the probability that the particle can be found between x = 0\cdot 45 and x = 0\cdot 55. Find the expectation value <x> of the particles position x = 0 to x = 1.

Derive energies and wave functions for motion of electron in a hydrogen atom.

Prove the following : (i) [L^2, L_x] = 0 (ii) [L_x, L_y] = i \hbar L_3

Draw a neat sketch showing potential wells and energy levels of the following : (i) Harmonic oscillator (ii) Hydrogen atom (iii) Particle in a box List the contrasting points and mention the variation of $E_n$' with n' of the above plots.

What is Zeeman effect? Explain Zeeman effect on the basis of classical electron theory.