List of top Physics Questions asked in GATE PH

Consider two real functions \[ U(x,y) = xy(x^2 - y^2), \] \[ V(x,y) = ax^4 + by^4 + cx^2y^2 + k, \] where $k$ is a real constant and $a, b, c$ are real coefficients. If $U(x, y) + i V(x, y)$ is analytic, then what is the value of $a \times b \times c$?

It is given that the electronic ground state of a diatomic molecule $X_2$ has even parity and the nuclear spin of $X$ is 0. Which one of the following is the CORRECT statement with regard to the rotational Raman spectrum ($J$ is the rotational quantum number) of this molecule?

For a transistor amplifier, the frequency response is such that the mid band voltage gain is 200. The cutoff frequencies are 20 Hz and 20 kHz. What is the ratio (rounded off to two decimal places) of the voltage gain at 10 Hz to that at 100 kHz?

In the vector model of angular momentum applied to atoms, what is the minimum angle in degrees (in integer) made by the orbital angular momentum vector and the positive z axis for a $2p$ electron?

Which of the following options represent(s) linearly independent pair(s) of functions of a real variable $x$?

The deuteron is a bound state of a neutron and a proton. Which of the following statements is/are CORRECT?

Which of the following is/are the CORRECT option(s) for the Joule-Thomson effect?

The Geiger-Muller counter is a device to detect $\alpha$, $\beta$, and $\gamma$ radiations. It is a cylindrical tube filled with monatomic gases like argon, and polyatomic gases such as ethyl alcohol. The inner electrode is along the axis of the cylindrical tube and the outer electrode is the tube. Which of the following statements is/are CORRECT?

A compound consists of three ions X, Y, and Z. The Z ions are arranged in an FCC arrangement. The X ions occupy $\frac{1}{6}$ of the tetrahedral voids and the Y ions occupy $\frac{1}{3}$ of the octahedral voids. Which one of the following is the CORRECT chemical formula of the compound?

Which one of the following is a dimensionless constant?

The atomic number of an atom is 6. What is the spectroscopic notation of its ground state, according to Hund’s rules?

Consider the potential $ U(r) $ defined as
\[ U(r) = -U_0 \frac{e^{-\alpha r}}{r} \] where $ \alpha $ and $ U_0 $ are real constants of appropriate dimensions. According to the first Born approximation, the elastic scattering amplitude calculated with $ U(r) $ for a (wave-vector) momentum transfer $ q $ and $ \alpha \to 0 $, is proportional to
(Useful integral: $ \int_0^\infty \sin(qr) e^{-\alpha r} \, dr = \frac{q}{\alpha^2 + q^2} $)

A system of two atoms can be in three quantum states having energies 0, $\epsilon$ and $2\epsilon$. The system is in equilibrium at temperature $ T = (k_B\beta)^{-1} $. Match the following Statistics with the Partition function.

Consider a single one-dimensional harmonic oscillator of angular frequency $ \omega $, in equilibrium at temperature $ T = \left( k_B \beta \right)^{-1 }$. The states of the harmonic oscillator are all non-degenerate having energy $ E_n = \left( n + \frac{1}{2} \right) \hbar \omega $ with equal probability, where $ n $ is the quantum number. The Helmholtz free energy of the oscillator is

Consider a particle in a one-dimensional infinite potential well with its walls at $ x = 0 $ and $ x = L $. The system is perturbed as shown in the figure. The first order correction to the energy eigenvalue is

The transition line, as shown in the figure, arises between $ 2D_{3/2} $ and $ 2P_{1/2} $ states without any external magnetic field. The number of lines that will appear in the presence of a weak magnetic field (in integer) is $\underline{\hspace{2cm}}$.

The normalized radial wave function of the second excited state of hydrogen atom is \[ R(r) = \frac{1}{\sqrt{24}} \left( \frac{a^{-3/2}}{r} \right) e^{-r/2a} \] \text{where $ a $ is the Bohr radius and $ r $ is the distance from the center of the atom. The distance at which the electron is most likely to be found is $ y \times a $. The value of $ y $ (in integer) is $\underline{\hspace{2cm}}$.}

Consider a system of three distinguishable particles, each having spin $ S = \frac{1}{2} $ such that $ S_z = \pm \frac{1}{2} $ with corresponding magnetic moments $ \mu_z = \pm \mu $. When the system is placed in an external magnetic field $ H $ pointing along the z-axis, the total energy of the system is $ \mu H $. Let $ x $ be the state where the first spin has $ S_z = \frac{1}{2} $. The probability of having the state $ x $ and the mean magnetic moment (in the +z direction) of the system in state $ x $ are

Consider a spin $ S = \hbar/2 $ particle in the state $ | \phi \rangle = \frac{1}{\sqrt{3}} | 2 \rangle + i | 2 \rangle $. The probability that a measurement finds the state with $ S_x = + \hbar/2 $ is

The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243.2 cm$^{-1}$. After excitation with a laser of wavelength 514.5 nm, the Stoke's line appeared at 17611.4 cm$^{-1}$ for a particular energy level. The wavenumber (rounded off to the nearest integer), in cm$^{-1}$, at which Stoke's line will appear for the next higher energy level is $\underline{\hspace{2cm}}$.

For a finite system of Fermions where the density of states increases with energy, the chemical potential