UPSC Physics Optional PYQs (CSE & IFoS)PYQs

For the logical equation given below, form the truth table and draw the corresponding logic circuit using different gates : Y = A \cdot B + \overline{A \cdot B}

How does the semi-empirical mass formula explain the stability of a nucleus against beta decay ?

Explain in detail the classification of elementary particles.

Explain why each of the following reactions is forbidden :

(i) p + p \rightarrow p + p + n

(ii) p + p \rightarrow p + \pi^+ + \gamma

(iii) \Xi^0 \rightarrow n + \pi^0

(iv) \Lambda \rightarrow p + \pi^0

(v) u_e + p \rightarrow n + e^+

What are the major components of a fission reactor ? With a schematic diagram explain its working.

Briefly explain the meson theory of nuclear force.

Calculate the energy released per gram of fuel for the nuclear reaction {}_1^2\text{H} + {}_1^2\text{H} \rightarrow {}_1^3\text{H} + {}_1^1\text{H}

{}_{14}^{27}\text{Si} and {}_{13}^{27}\text{Al} are mirror nuclei. Their ground states are identical except the charge. If their mass difference is 6\text{ MeV}, estimate their radius neglecting the proton-neutron mass difference.

Discuss the different coupling schemes in atomic spectroscopy with suitable diagrams.

An atom in an excited state of 4\cdot 7\text{ eV} emits a photon and ends up in the ground state. The lifetime of the excited state is 10^{-13}\text{ s}. Calculate the energy uncertainty and obtain the spectral line width in wavelength of photon.

What is Lamb shift ? How is it measured ?

What are the characteristics of a Raman spectrum ? How do you study Raman spectra in the laboratory ? Give two applications of Raman effect.

Explain spin-spin and spin-lattice relaxation times in NMR spectroscopy. How do they influence the line width of the NMR line ?

Given that the rotational inertia of \text{HCl} molecule has the value I = 2\cdot 66 \times 10^{-47}\text{ kg-m}^2, estimate the energy difference between the lowest and first excited state of \text{HCl}.

How is proton magnetic resonance applied to determine the chemical shifts in molecules containing hydrogen atom ? Illustrate your answer with a suitable example.

Explain the origin of the anomalous Zeeman effect.

Show that

(i) no two of the three components of angular momentum operator commute and

(ii) the third component of the angular momentum operator commutes with the square of angular momentum operator.

Derive an expression for transmission coefficient for a particle through a rectangular potential barrier.

Normalize the ground state wave function \psi_0(x) = A e^{(-\alpha x^2/2)} for the simple harmonic oscillator and find expectation values \langle x \rangle and \langle x^2 \rangle.

Using WKB approximation find out the lifetime of \alpha-emitter.