UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A nuclear reactor using {}^{235}_{92}\text{U} is to operate at a power level of 250 megawatt. If the energy released per fission of {}^{235}_{92}\text{U} is 200\text{ MeV}, calculate the rate of consumption per year.

Explain the classification of elementary particles and discuss their interactions.

(i) Write semi-empirical mass formula for the nuclei. Discuss in brief the physical significance of each term. (ii) The meson theory of nuclear forces assumes the virtual exchange of pions. If a nucleon emits a virtual pion of rest mass 270\text{ m}_{\text{e}}, calculate the range of the nuclear force. (\text{m}_{\text{e}} is the mass of electron = 9\cdot 11 \times 10^{-31}\text{ kg})

Show that pion decay, muon decay and pair production conserve the Lepton numbers \text{L}_{\text{e}} and \text{L}_{\mu}.

(i) Plot proton number (Z) versus neutron number (N). What is the inference from the plot with regards to light and heavy nuclides ? (ii) Which nucleus would you expect to be more stable, {}^{7}_{3}\text{Li} or {}^{8}_{3}\text{Li} ? Justify your answer.

Discuss in brief any two basic nuclear properties. Find the nuclear radius of {}^{12}_{6}\text{C} nucleus. Compare the atomic radius of carbon C-12 to the nuclear radius assuming the atomic radius to be 0\cdot 529 \times 10^{-10}\text{ m}. (R_0 = 1\cdot 2\text{ fm}) What inference will you get from the comparison with regards to nuclear size of carbon ?

(i) Plot mass number A versus binding energy per nucleon. How does this curve help to explain the nuclear fission and fusion ? (ii) In their old age, heavy stars obtain part of their energy by the following nuclear reaction {^{4}_{2}\text{He}} + {^{12}_{6}\text{C}} = {^{16}_{8}\text{O}}. How much energy does each such event give off ? [\text{Given : } {^{4}_{2}\text{He}} = 4\cdot 002603\text{ u}, {^{12}_{6}\text{C}} = 12\cdot 000000\text{ u}, {^{16}_{8}\text{O}} = 15\cdot 999\text{ u}]

Explain the principle and working of Stern-Gerlach Experiment.

A Raman line associated with a vibrational mode which is both Raman and infrared active is found at 4600\text{ \AA} when excited by light of wavelength 4358\text{ \AA}. Calculate the wavelength of the corresponding infrared band.

Obtain an expression for the rotational energy levels of a diatomic molecule, taking it as a rigid rotator. Discuss its spectrum and the selection rule.

Explain the mechanism of Fluorescent emission of radiation. Distinguish between Fluorescence spectra and Raman spectra of a diatomic molecule.

The calcium line of wavelength \lambda = 4226\cdot 73\text{ \AA} (\text{P} \rightarrow \text{S}) exhibits normal Zeeman splitting when placed in a uniform magnetic field of 4\text{ Weber/metre}^3. Calculate the wavelength of three components of normal Zeeman pattern and the separation between them.

Prove the following : (i) [L^2, L_x] = 0 (ii) [L_x, L_y] = i \hbar L_3

(i) What do you mean by expectation value of a physical quantity ? How does it help to extract information from a wave function ? (ii) A particle limited to move along x-axis has the wave function \psi = ax between x = 0 and x = 1, \psi = 0 elsewhere. Find the probability that the particle can be found between x = 0\cdot 45 and x = 0\cdot 55. Find the expectation value <x> of the particles position x = 0 to x = 1.

Derive energies and wave functions for motion of electron in a hydrogen atom.

(i) Discuss about the validity criterion for the WKB approximation. (ii) Qualitatively explain alpha (\alpha) particle emission by WKB approximation.

What is Normal Zeeman effect ? Give the classical interpretation of Normal Zeeman effect.

(i) Draw a neat sketch of a finite rectangular potential barrier well of height U' and width L' that contains a particle whose energy E' is less than U'. Solve the Schrödinger equations of the particles outside the well. (ii) Plot wave functions and probability densities |\psi|^2 of the particle for the first three states. Compare the results with that of a particle in a box of infinite potential (U = \infty).

Draw a neat sketch showing potential wells and energy levels of the following : (i) Harmonic oscillator (ii) Hydrogen atom (iii) Particle in a box List the contrasting points and mention the variation of $E_n$' with n' of the above plots.

(i) State and explain position momentum uncertainty principle. Justify that this principle is not just a negative statement rather a useful tool, with one example. (ii) The lifetime of an excited state of an atom is about 10^{-8}\text{ sec.} Calculate the minimum uncertainty in the energy of the excited state.