UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Draw the crystal structure of \text{CaF}_2 indicating the positions of cations and anions. What are their respective coordination numbers?

Consider the BJT amplifier circuit given below with the following parameters : d.c. current gain \beta_{\text{dc}} = a.c. current gain \beta_{\text{ac}} = 100 \text{I}_\text{B} = 20\ \mu\text{A} for \text{V}_\text{B} = 0\cdot 7\text{ V}, and \text{i}_\text{b} = \pm 2\ \mu\text{A} for \text{v}_\text{i} = \pm 10\text{ mV}. Determine the values of \text{V}_{\text{CE}}, input impedance and voltage gain \text{A}_\text{v}.

What will be the frequency of Josephson current, if a d.c. voltage of 4\cdot 0\ \mu\text{V} is applied across a Josephson junction?

Explain Gell-Mann and Ne'eman SU(3) symmetry for the classification of elementary particles — baryons and mesons.

On the basis of conservation laws, explain whether the following reactions are allowed or forbidden : (i) \pi^- + \text{p} \longrightarrow \Sigma^+ + \text{K}^- (ii) \text{K}^- + \text{p} \longrightarrow \Omega^- + \text{K}^+ + \text{K}^0 (iii) \Omega^- \longrightarrow \Xi^0 + \pi^- (iv) \pi^+ + \text{p} \longrightarrow \text{p} + \text{p} + \bar{\text{n}} (v) \Sigma^+ \longrightarrow \Lambda^0 + \text{K}^+

Justify the fact that the electrons are emitted from nuclei in \beta-decay but they cannot be contained inside the nuclei.

Why does a neutron star have a magnetic field if it is composed of neutrons?

What do you understand by the critical size of a nuclear reactor? Write down the common features of nuclear reactors used for the production of electricity.

The nature of curves of binding energy and packing fraction are complementary to each other. Explain.

Derive an expression for \alpha-disintegration energy for a nucleus in a radioactive decay process.

Evaluate the Landé g-factor for the {}^3\mathrm{P}_1 level in the 2p 3s configuration of the {}^6\mathrm{C} atom, and then calculate the splitting of the level in eV, when the atom is in an external magnetic field of 0.2 tesla.

What is vector model of the atom? On the basis of it, explain the L-S and j-j coupling under external magnetic field.

An atomic state is denoted by {}^4\mathrm{D}_{5/2}. What should be the minimum number of electrons involved for this state? Give a possible electron configuration.

(i) Homonuclear diatomic molecules do not give any pure rotational or vibrational spectra, whereas they do give a rotational Raman spectra. Comment. (ii) The separation between the adjacent rotational Raman lines is 4B in hydrogen molecule, whereas in oxygen molecule it is 8B. Why?

How does the Stern-Gerlach experiment explain the concept of electron spin and its angular momentum quantization?

The rotational and centrifugal distortion constants of a diatomic molecule are 10\cdot 59\text{ cm}^{-1} and 5\cdot 3 \times 10^{-4}\text{ cm}^{-1}, respectively. Obtain an estimate each for the vibrational frequency and force constant of the molecule. [\text{Given } : \text{The reduced mass of the molecule is } 1\cdot 626 \times 10^{-27}\text{ kg}]

Discuss the influence of anharmonicity on the vibrational spectra of diatomic molecules with necessary diagrams.

Often the intensity of rotational transition J = 0 \to J = 1 is not the most intense. Explain.

For the n^{\text{th}} state of linear harmonic oscillator, evaluate the uncertainty product (\Delta x) \cdot (\Delta p).

Evaluate the commutator \left[\frac{\partial^2}{\partial x^2}, x\right] and hence show that [p^2, x] = -2 i\hbar p.