UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Describe how Davisson-Germer electron diffraction experiment confirms the de Broglie hypothesis of matter wave.

Find the energy Ligenvalues of a one dimensional harmonic oscillator whose Hamiltonian is given by H = \frac{P^2}{2m} + \frac{1}{2} k x^2

With incident X-rays of wavelength 1.618\text{ \AA} Compton scattering is observed at 90^\circ from the incident beam. Calculate. (i) the wavelength of Compton radiation, and (ii) the angle at which the recoil electron may be observed. In what state should the electrons be in Compton scattering?

What values of J quantum number may be observed in normal atoms of alkalis and alkaline earths ? Which of the spectral lines in alkaline earth would show normal Zeeman effect and why?

Using de Broglie's relation, deduce an expression for energy values of a particle enclosed in a one-dimensional box. 'Free electrons' in a long-chain molecule may be treated as particles in a one-dimensional box. From a long-chain molecule of length 60\text{ \AA} deduce the lowest three energy state values in eV units.

Derive an expression for the magnetic moment of an electron in an atom taking into account electron-spin. Explain anomalous Zeeman effect by considering the above magnetic moment.

Using Schrodinger's equation show that a free particle in a box can have only discrete energy values.

Draw energy diagram for transverse Zeeman effect for D line of sodium 3^2P_{3/2} \rightarrow 3^2S_{1/2}

State the important characteristics of photoelectric effect and indicate how they are in conflict with classical ideas but are explained on the basis of quantum theory.

What are de Broglie waves? State the uncertainty principle and explain its relation with de Broglie waves by considering a free particle.

In a Compton effect experiment with incident X-ray of wavelength 0.060\text{ \AA}, one recoil electron had energy 4100\text{ eV}. Calculate the corresponding angle of scattering and the wavelength of the scattered radiation (Standard formulae may be assumed.)

Set up Schrodinger's equation for a free particle confined in a cubical box and find the energy eigenvalues. What form will Pauli principle take for electrons in such a box? Deduce the zero point energy if the length of the box be 10^{-10}\text{ metre} and there be 10 electrons in it. (The coulomb interaction maybe disregarded.)

A photon of energy 10\text{ eV} is scattered by an electron having an initial velocity of 1000\text{ km s}^{-1}. After the scattering the electron velocity is reduced to 200\text{ km s}^{-1}. Deduce the energy of the scattered photon.

What is the value of the spin of the electron and the corresponding magnetic-moment? Can that be considered as arising from the classical case of rotation of a finite rigid charged body about its axis? Give reasons for your answer.

State the important points in Bohr's theory of the hydrogen atom winch depart from classical ideas. Flow is the idea of Bohr orbits changed in Schrodinger's wave mechanics?

State de Brogue hpotliesis and use it to deduce the energy levels of a particle in a one-dimensional box. Calculate the mean energy per electron at 0\text{ K} if electrons arc enclosed in a long-chain molecule of length 50\text{ \AA}.

Set up Schrodinger's equation for a one dimensional harmonic oscillator. Assuming that the solution is of the from \psi = A e^{-\alpha x^2} f(x) where \alpha is a constant and f(x) is a polynomial in x, find the energy eigen values and the ground state eigenfunction. Comment on the relation between the ground slate energy and Heisenberg's uncertainty principle.

In a Compton scattering the angle of scattering was 30^\circ while the angle of recoil was 60^\circ. Calculate the energy of the incident photon taking the formulae you use as given.

Write down Schrodinger's equation in one-dimension and explain the significance of the eigenvalues and eigenfunction of this equation. Solve the Schrodinger's equation if the potential function V is given as V(x) = V_e(\text{a constant}) for |x| < a/2 = 0 for |x| > a/2 State the boundary conditions you use along with their justification (In the solution consider particles incident from one side only.) If he total energy F < V_0 show that there is an important difference with classical mechanics. Explain with the help of the uncertainty principle that E < V_0 does not mean that the kinetic energy is negative.

Photoelectron are liberated by ultraviolet light of wavelength 3000\text{ \AA} from a metallic surface for which the photoelectric threshold is at 4000\text{ \AA}. Calculate the De Broglie wavelength of electrons emitted with maximum kinetic energy.