List of top Physics Questions asked in GATE PH

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:
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:
Consider a crystal that has a basis of one atom. Its primitive vectors are \( \vec{a}_1 = a\hat{i} \), \( \vec{a}_2 = a\hat{j} \), \( \vec{a}_3 = \frac{a}{2}(\hat{i} + \hat{j} + \hat{k}) \), where \( \hat{i}, \hat{j}, \hat{k} \) are the unit vectors in the \( x \), \( y \), and \( z \) directions of the Cartesian coordinate system and \( a \) is a positive constant. Which one of the following is the correct option regarding the type of the Bravais lattice?
For a two-dimensional hexagonal lattice with lattice constant \( a \), the atomic density is:

An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of \( \frac{2\pi}{n} \), is identical to the original.
Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen? 
 

A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of the following options displays the color codes that are consistent with the color model?