UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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

Show that nucleus is a quantum system.

Find the total kinetic energy of electron and antielectron neutrino emitted in beta decay of free neutron. (The neutron-proton mass difference is 1.30\,\mathrm{MeV} and mass of electron is 0.51\,\mathrm{MeV})

{}^{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.

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

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

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)

Discuss pure rotational spectra of linear molecules.

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 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

What is Lamb shift?

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

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.

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.

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})

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

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

Calculate (\Delta x)^2, where \Delta x = x - \langle x \rangle.

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.

Write down the expressions for Bose-Einstein and Fermi-Dirac distribution functions, and show how Fermi-Dirac distribution leads to the explanation of Pauli's exclusion principle.