UPSC Physics Optional PYQs (CSE & IFoS)PYQs

(ii) From a study of the radial part of the Schrödinger equation of a deuteron for any angular momentum l, what do we conclude?

Write the decay reactions of the neutral pions (\pi^0) and the charged pions (\pi^+, \pi^-).

A sample contains 4\text{ mg} of {}^{210}\text{Bi}. If the half-life of radioactive {}^{210}\text{Bi} is 5\text{ days} and the average energy of the \beta-particles emitted is 0\cdot 34\text{ MeV}, then at what rate does the sample emit energy?

In the case of deuterons, answer the following : (i) What percentage of the time do the nucleons of a deuteron spend within the range of the nuclear forces?

What is meant by strength of the interactions of elementary particles ? Classify the different forces on the basis of this strength of interaction.

(ii) \bar{\nu}_e + p^+ \rightarrow n^0 + e^- What are the various conservation laws for elementary particles ? Apply these conservation laws to confirm whether the following reactions are possible or not : (i) \pi^+ + n^0 \rightarrow K^0 + K^+ (ii) \bar{\nu}_e + p^+ \rightarrow n^0 + e^-

Apply the meson theory of nuclear forces to write the interaction between protons, neutrons, proton to neutron and neutron to proton.

Compare nuclear density of hydrogen ({}_1\text{H}^1) with its atomic density. (Assume the atom to have the radius of its first Bohr orbit). What inference can one get from the above comparison ?

Does the nucleus possess magnetic moment ? Justify your answer. Define nuclear magneton (\mu_{\text{N}}) and Bohr magneton (\mu_{\text{B}}). Calculate their values.

(i) Write semi-empirical mass formula. Calculate the atomic number (Z) of most stable nucleus for given mass number (A) using the above formula. (Use the value of fitted coefficients for Coulomb energy a_3 = 0\cdot 711\text{ MeV} and that for asymmetry energy a_4 = 23\cdot 702\text{ MeV}). (ii) Calculate the Q-value of the following nuclear reaction : {}_4\text{Be}^9 + {}_2\text{He}^4 = {}_6\text{C}^{12} + {}_0\text{n}^1 Given : the mass of neutral atoms of \text{Be}, \text{He} and \text{C} are 9\cdot 015060, 4\cdot 003874 and 12\cdot 003815\text{ amu}, respectively. The mass of neutron is 1\cdot 008986\text{ amu}.

For the ground state of deuteron, prove that the radius of nucleon is of the order of \sim 2\cdot 15 \times 10^{-13}\text{ cm}.

A radionuclide (N_1) decays to a radioactive daughter (N_2) that subsequently decays to a third daughter (N_3). If at t = 0, the initial concentrations of N_1, N_2 and N_3 are N_1^0, 0 and 0 respectively, and the decay constants are \lambda_1 (from N_1 \rightarrow N_2) and \lambda_2 (from N_2 \rightarrow N_3), then derive the expression for N_2 at time t. Given that the daughter N_3 is stable.

What were the difficulties faced by the initial theory of \beta-decay? How did Pauli eliminate the difficulties? What were the expected properties of the new particle proposed by Pauli?

What is the age of a fossil that contains 6\text{ g} of carbon {}^{14}\text{C} and has a decay rate of 27\text{ decays per minute} ? Given : Ratio \frac{{}^{14}\text{C}}{{}^{12}\text{C}} = 1\cdot 3 \times 10^{-13}, Half life (T_{1/2}) of {}^{14}\text{C} = 5730\text{ yrs}.

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

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

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.

Establish the Rutherford's scattering cross section formula for \alpha-particle by considering the standard assumptions and symbols.

How could you establish that \nu_e and \bar{\nu}_e are two different particles ?

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