List of top Questions asked in GATE PH

Two projectile protons \( P_1 \) and \( P_2 \), both with spin up (along the \( +z \)-direction), are scattered from another fixed target proton \( T \) with spin up at rest in the \( xy \)-plane, as shown in the figure. They scatter one at a time. The nuclear interaction potential between both the projectiles and the target proton is \( \hat{\lambda} \vec{L} \cdot \vec{S} \), where \( \vec{L} \) is the orbital angular momentum of the system with respect to the target, \( \vec{S} \) is the spin angular momentum of the system, and \( \lambda \) is a negative constant in appropriate units. Which one of the following is correct?


 

The figure shows a system of two equal masses \( m \) and three massless horizontal springs with spring constants \( k_1 \), \( k_2 \), and \( k_1 \). Ignore gravity. The masses can move only in the horizontal direction, and there is no dissipation. If \( m = 1 \), \( k_1 = 2 \), and \( k_2 = 3 \) (all in appropriate units), the frequencies of the normal modes of the system in the same system of units are:


 

The wire loop shown in the figure carries a steady current \( I \). Each straight section of the loop has length \( d \). A part of the loop lies in the \( xy \)-plane and the other part is tilted at \( 30^\circ \) with respect to the \( xz \)-plane. The magnitude of the magnetic dipole moment of the loop (in appropriate units) is:


 

The screened nuclear charge of neutral Helium atom is given as \( 1.7e \), where \( e \) is the magnitude of the electronic charge. Assuming the Bohr model of the atom for which the energy levels are \( E_n = - \frac{Z^2}{2n^2} \) atomic units (where \( Z \) is the atomic number), the first ionization potential of Helium in atomic units is:

Consider a monatomic chain of length 30 cm. The phonon density of states is \( 1.2 \times 10^{-4} \) s. Assuming the Debye model, the velocity of sound in m/s (rounded off to one decimal place) is 

Powder X-ray diffraction pattern of a cubic solid with lattice constant \( a \) has the (111) diffraction peak at \( \theta = 30^\circ \). If the lattice expands such that the lattice constant becomes \( 1.25a \), the angle (in degrees) corresponding to the (111) peak changes to \( \sin^{-1} \left( \frac{1}{n} \right) \). The value of \( n \) (rounded off to one decimal place) is _________

The effective magnetic moment (in units of Bohr magneton) for the ground state of an isolated 4𝑓 ion with 6 unpaired electrons in the 4𝑓 shell according to Hund’s rules is (in integer) _____

A linear dielectric sphere of radius \( R \) has a uniform frozen-in polarization along the \( z \)-axis. The center of the sphere initially coincides with the origin, about which the electric dipole moment is \( \vec{p}_1 \). When the sphere is shifted to the point \( (2R, 0, 0) \), the corresponding dipole moment with respect to the origin is \( \vec{p}_2 \). The value of \( \left| \frac{\vec{p}_1}{\vec{p}_2} \right| \) (in integer) is:
One mole of an ideal monatomic gas at absolute temperature \( T \) undergoes free expansion to double its original volume, so that the entropy change is \( \Delta S_1 \). An identical amount of the same gas at absolute temperature \( 2T \) undergoes isothermal expansion to double its original volume, so that the entropy change is \( \Delta S_2 \). The value of \( \frac{\Delta S_1}{\Delta S_2} \) (in integer) is:
Nuclear radiation emitted from a \( {Co}^{60} \) radioactive source is detected by a photomultiplier tube (PMT) coupled to a scintillator crystal. Which of the following option(s) is/are correct?
Potential energy of two diatomic molecules P and Q of the same reduced mass is shown in the figure. According to this diagram, which of the following option(s) is/are correct?
Which of the following consideration(s) is/are showing that nuclear beta decay, \( n \to p + e^{-} + \bar{\nu}_e \), has to be a three-body decay?

A schematic Pressure-Temperature diagram of water is shown in the figure. Which of the following option(s) is/are correct?


 

Which of the following option(s) is/are correct for photons?
Which of the following option(s) is/are correct for the ground state of a hydrogen atom?
A paramagnetic material containing paramagnetic ions with total angular momentum \( J = \frac{1}{2} \) is kept at absolute temperature \( T \). The ratio of the magnetic field required for 80% of the ions to be in the lowest energy state to that required for having 60% of the ions to be in the lowest energy state at the same temperature is:
Consider one mole of a monovalent metal at absolute zero temperature, obeying the free electron model. Its Fermi energy is \( E_F \). The energy corresponding to the filling of \( \frac{N_A}{2} \) electrons, where \( N_A \) is the Avogadro number, is \( 2^n E_F \). The value of \( n \) is:
Consider the function \( f(z) = \frac{1}{z^2 (z - 2)^3} \) of a complex variable \( z \).
The residues of the function at \( z = 0 \) and \( z = 2 \), respectively, are:
The nuclear energy levels of mirror nuclei are similar. Using this empirical fact alone, the nuclear force can be said to be independent of which one of the following properties of the nucleons?

A logic gate circuit is shown in the figure below. The correct combination for the input \( (P, Q) \) for which the output \( T = 1 \) is:


 

Which one of the following baryons has strangeness quantum number \( S = -1 \)?
As per the Drude model of metals, the electrical resistance of a metallic wire of length \( L \) and cross-sectional area \( A \) is:
(Consider \( \tau \) as the relaxation time, \( m \) as electron mass, \( n \) as carrier concentration, and \( e \) as electronic charge)
Which one of the following is correct for the phase velocity \( v_p \) and group velocity \( v_g \)? (c is the speed of light in vacuum)
The Joule-Thomson expansion of a gas is:
A particle of mass \( m \) is in a potential \( V(x) = \frac{1}{2} m \omega^2 x^2 \) for \( x > 0 \), and \( V(x) = \infty \) for \( x \leq 0 \), where \( \omega \) is the angular frequency. The ratio of the energies corresponding to the lowest energy level to the next higher level is: