UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Explain spin-spin and spin-lattice relaxation times in NMR spectroscopy. How do they influence the line width of the NMR line ?

How is proton magnetic resonance applied to determine the chemical shifts in molecules containing hydrogen atom ? Illustrate your answer with a suitable example.

What are the characteristics of a Raman spectrum ? How do you study Raman spectra in the laboratory ? Give two applications of Raman effect.

Discuss the vibrational spectra of a diatomic molecule treating it as an anharmonic oscillator.

Obtain an expression for the resonance condition in NMR.

Given that the spacing between vibrational levels of CO molecules is 8.45 \times 10^{-2}\ \mathrm{eV} of energy. Find the force constant of the molecule.

A sample of a certain element is placed in a magnetic field of flux density 0.3 tesla. How far apart is the Zeeman component of a spectral line of wavelength 4500\mathring{\mathrm{A}}? Given : e/m = 1.76 \times 10^{11}\ \mathrm{c/kg}, c = 3.0 \times 10^8\ \mathrm{m\,s^{-1}}.

What is Lamb shift ? How is it measured ?

Explain the relaxation processes in NMR spectroscopy.

Obtain an expression for the normal Zeeman shift. Illustrate the Zeeman splitting of spectral lines of H atom and the allowed transitions for the l = 1 and l = 2 states.

Normalize the ground state wave function \psi_0(x) = A e^{(-\alpha x^2/2)} for the simple harmonic oscillator and find expectation values \langle x \rangle and \langle x^2 \rangle.

Derive an expression for transmission coefficient for a particle through a rectangular potential barrier.

Show that

(i) no two of the three components of angular momentum operator commute and

(ii) the third component of the angular momentum operator commutes with the square of angular momentum operator.

What is the de Broglie wavelength of an electron whose kinetic energy is 100\text{ eV} ?

Using WKB approximation find out the lifetime of \alpha-emitter.

Using the commutation relations [x,p_x]=[y,p_y]=[z,p_z]=i\hbar deduce the commutation relation between the components of angular momentum operator \mathbf{L}. [L_x,L_y]=i\hbar L_z [L_y,L_z]=i\hbar L_x\quad\text{and}\quad [L_z,L_x]=i\hbar L_y.

Obtain the time-dependent Schrödinger equation for a particle. Hence deduce the time independent Schrödinger equation.

The mean life of Lambda (\Lambda^0) particle is 2.6 \times 10^{-10}\,\mathrm{s}. What will be the uncertainty in the determination of its mass in \mathrm{eV}?

Solve the Schrödinger equation for a particle of mass m confined in one dimensional potential well of the form: V(x)= \begin{cases} 0; & 0 \leq x \leq L,\\ \infty; & x<0,\ x>L. \end{cases} Obtain the discrete energy values and the normalized eigen functions.

Find the de Broglie wave length of

(i) a neutron

(ii) an electron moving with kinetic energy of 500\,eV (1\,eV = 1.602 \times 10^{-19}\,J)