UPSC Physics Optional PYQs (CSE & IFoS)PYQs

{}^{235}\mathrm{U} yields two fragments of A=95 and A=140. Obtain the energy distribution of the fission products. Assume that the two fragments are ejected with equal and opposite momentum.

What are chain reactions? What do you mean by critical size of the core in which chain reactions take place? What is critical mass?

Treating a diatomic molecule as a simple harmonic oscillator, obtain its vibrational energy levels.

The wavelengths (\lambda) in the visible spectrum of H atom can be expressed by the empirical formula \lambda = \left( \frac{n_1^2}{n_1^2 - 4} \right) \cdot G where n_1 is an integer and n_1 = 3, 4 etc. and G is an empirical constant. Prove from the above, the wave number \bar{\nu} = R_H \left( \frac{1}{2^2} - \frac{1}{n_1^2} \right), \text{ where } R_H = \frac{4}{G}.

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

Give the elementary theory of NMR. Explain the two different relaxation processes.

What is the mechanism of emission of light in fluorescent lamps and in painted signboards ? Explain.

Discuss pure rotational spectra of linear molecules.

The observed vibrational frequency of the \mathrm{CO} molecule is 6.42 \times 10^{13}\ \mathrm{Hz}. What is the effective force constant of this molecule? (Mass of carbon atom = 12u and mass of oxygen atom = 16u, where u is atomic mass unit)

Obtain the term symbols for two singlet states and two triplet states for two electron atoms.

Discuss the fine structure of hydrogen atom spectrum. Draw the compound doublet spectrum arising as a result of transitions between {}^2P and {}^2D levels.

What is Lamb shift?

What do you mean by ‘term symbols’? Obtain term symbols for the following sets of values of S and L:

(i) S=\frac{1}{2},\ L=2

(ii) S=1,\ L=1

(iii) S=\frac{3}{2},\ L=1

Solve the Schrödinger equation for a particle of mass m in an infinite rectangular well defined by V(x)=\begin{cases} 0\ ;\ 0\leq x\leq L\\ \infty\ ;\ x<0,\,x>L \end{cases} Obtain the normalized eigen functions and the corresponding eigen values.

The normalized wave function for the electron in the ground state of the hydrogen atom is given by \psi(r)=\frac{1}{(\pi a_0^3)^{1/2}}e^{-r/a_0} where a_0 is the radius of the first Bohr orbit. Calculate \langle r\rangle and \left\langle\frac{1}{r}\right\rangle.

Let \vec{\sigma} be the vector operator with component equal to Pauli's spin matrices \sigma_x,\sigma_y,\sigma_z. If \vec{a} and \vec{b} are vectors in 3D space, prove the identity (\vec{\sigma}\cdot\vec{a})(\vec{\sigma}\cdot\vec{b})=\vec{a}\cdot\vec{b}+i\vec{\sigma}\cdot(\vec{a}\times\vec{b})

Show that {}^2S_{\frac{1}{2}}, {}^2P_{\frac{1}{2}} and {}^2P_{\frac{3}{2}} levels of sodium spectrum are split in the ratio of 3:1:2 due to anomalous Zeeman effect.

On the basis of uncertainty principle calculate the size of Hydrogen atom.

For a quantum mechanical system prove that all energy eigen-values E_n are real and if E_n \neq E_k, then the corresponding eigen functions are orthogonal.

Solve the eigen value equation L^2 Y(\theta, \phi) = \lambda \hbar^2 Y(\theta, \phi) and obtain the eigen values and eigen functions of L^2.