PYQ Bank

(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}.

What is nuclear resonance absorption of gamma rays ? Describe the working and applications of Mossbauer spectrometer.

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}.

(ii) From a study of the radial part of the Schr"{o}dinger equation of a deuteron for any angular momentum l, what do we conclude?

(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^-

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?

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?

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 ?

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

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?

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

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

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}.

What do you understand by the critical size of a reactor ? Explain the main features of nuclear reactors.

What do you understand by nuclear forces ? Explain meson theory of exchange forces.

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

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

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