List of top Nuclear and Particle Physics Questions asked in GATE PH

Consider the induced nuclear fission reaction:
\[ {}^{235}_{92}\text{U} + n \rightarrow {}^{93}_{37}\text{Rb} + {}^{141}_{55}\text{Cs} + 2n \]
where neutron momenta in both initial and final states are negligible. The ratio of the kinetic energies (KE) of the daughter nuclei,
\[ \frac{\text{KE}({}^{93}_{37}\text{Rb})}{\text{KE}({}^{141}_{55}\text{Cs})} \]
is __________.
Binding energy and rest mass energy of a two-nucleon bound state are denoted by \( B \) and \( mc^2 \), respectively, where \( c \) is the speed of light. The minimum energy of a photon required to dissociate the bound state is _______.
According to the nuclear shell model, the absolute value of the difference in magnetic moments of \({^{15}_{8}O}\) and \({^{15}_{7}N}\), in the units of nuclear magneton (\(\mu\)), is \(\frac{a}{3}\). The magnitude of \(a\) is (in integer).
Let P, Q and R be three different nuclei. Which one of the following nuclear processes is possible?

For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respectively, choose the best suited interpretation. 

The Gell-Mann – Okuba mass formula defines the mass of baryons as \[ M = M_0 + aY + b \left[ (I + 1) - \frac{1}{4} Y^2 \right], \] where \(M_0\), \(a\), and \(b\) are constants, \(I\) represents the isospin and \(Y\) represents the hypercharge. If the mass of \(\Sigma\) hyperons is the same as that of \(\Lambda\) hyperons, then the correct option(s) is(are)
For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices \( \sigma_1, \sigma_2 \) for particles 1 and 2, respectively. The value of \( \sigma_1 \cdot \sigma_2 \) (in integer) is \(\underline{\hspace{2cm}}\).
The Coulomb energy component in the binding energy of a nucleus is 18.432 MeV. If the radius of the uniform and spherical charge distribution in the nucleus is 3 fm, the corresponding atomic number (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\).
\text{(Given: } \frac{e^2}{4 \pi \epsilon_0} = 1.44 \, \text{MeV fm}).}
A linear charged particle accelerator is driven by an alternating voltage source operating at 10 MHz. Assume that it is used to accelerate electrons. After a few drift-tubes, the electrons attain a velocity \( 2.9 \times 10^8 \, \text{m/s} \). The minimum length of each drift-tube, in m, to accelerate the electrons further (rounded off to one decimal place) is \(\underline{\hspace{2cm}}\).
Assume that \(^{13}N (Z = 7)\) undergoes first forbidden \( \beta^+ \) decay from its ground state with spin-parity \( J_i^\pi \), to a final state \( J_f^\pi \). The possible values for \( J_i^\pi \) and \( J_f^\pi \), respectively are
In an experiment, it is seen that an electric-dipole (E1) transition can connect an initial nuclear state of spin-parity \( J_i^\pi = 2^+ \) to a final state \( J_f^\pi \). All possible values of \( J_f^\pi \) are