PYQ Bank

Explain conservation of Baryon Number. Comment on the stability of proton.

What type of interaction takes place in the following reactions and justify your answer. (i) \mu^- \longrightarrow e^- + u_e + \bar{\nu}_\mu (ii) p + \mu^- \longrightarrow n + u_\mu

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

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

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

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

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

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

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

What is Lamb shift?

Discuss pure rotational spectra of linear molecules.

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}.

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)

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.

Solve the Schrodinger equation for a potential step function given by \begin{aligned} v(x) &= 0 \text{ for } x < 0 \\ &= v_0 \text{ for } x > 0 \end{aligned} and calculate the reflection and transmission coefficients. Show that for E < v_0 there is a finite probability of finding the particle in a classically forbidden region.

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

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})

Estimate the size of the hydrogen atom and the ground state energy from the uncertainty principle.

Calculate the wavelength of de Broglie waves associated with electrons accelerated through a potential difference of 200 Volts.

Normalize the wave function \psi(x)=e^{-\lvert x\rvert}\sin\alpha x