24 Official GATE PH Questions with Verified Solutions & Answer Keys
An atomic state of hydrogen is represented by the following wavefunction: $\psi(r, \theta, \phi) = \frac{1}{4\sqrt{2\pi}} \left(\frac{1}{a_0}\right)^{3/2} \left(2 - \frac{r}{a_0}\...
Let (Vo) denote the ground state of the hydrogen atom. Choose the correct statement from those given below: (A) [Lx, Ly] |Vo) =0 (B) F (v.)=0 (C) [\cdotS|vo)#0 (D) [Sx, Sy] (%o) =0...
The radial wave function of the electrons in the state of n=1 and /=0 in a hydrogen atom is R,o =\cdot ao 2, еxр , ao is the Bohr radius. The most probable value of r for an electr...
Let n)and P) denote the isospin states with 1 = ½, Is = ½/ and 1 = ½/ , lz = -½ of a nucleon respectively. Which one of the following two-nucleon states has I= 0, I,= 0 ? (A) ((nn)...
The polarizability of the hydrogen atom in unit of (C2m/N) is (A) 2.0 10-40 (B) 1.4 10-41 (C) 1.4 10-40 (D) 2.0 10-39 Statement for Linked Answer Questions 54 and 55: A par...
0,, 0, and o, are the Pauli matrices. The expression 2o,o, + o,0, is equal to (A) - 3iо, (B) - io: (C) io, (D) 3io,...
Positronium is an atom made of an electron and a position. Given the Bohr radius for the ground state of the Hydrogen atom to be 0.53 Angstroms, the Bohr radius for the ground stat...
(B) imaginary (C) of modulus one (D) real and positive Which one of the following represents the 3p radial wave function of hydrogen atom? (ao is the Bohr radius) (A) (R(r) (B) 1R(...
The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (ao is the Bohr radius) (A) - Зеао (B) zero (C) eao (D) 3eao...
(A) (B) (C) (D) For a finite system of Fermions where the density of states increases with energy, the chemical potential decreases with temperature increases with temperature does...
(A) The free energy of a ferromagnet is given by F = Fo + ao(T - Tc)M? + bM*, where Fo, do, and b are positive constants, M is the magnetization, T is the temperature, and Tc is th...
For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices 01, 0z for particles 1 and 2, respectively. The value of (01 \cdot 02) (in intege...
The normalized radial wave function of the second excited state ($n = 3, l = 0$) of hydrogen atom is $R(r) = \frac{2}{(3a)^{3/2}} \left( 1 - \frac{2r}{3a} + \frac{2r^2}{27a^2} \rig...
An excited state of Ca atom is [Mg]3p54s23d1. The spectroscopic terms corresponding to the total orbital angular momentum are...
From the pairs of operators given below, identify the ones which commute. Here l and j correspond to the orbital angular momentum and the total angular momentum, respectively....
Pauli spin matrices satisfy (A) σα σβ - σβ σα = i εαβγ σγ (B) σα σβ - σβ σα = 2i εαβγ σγ (C) σα σβ + σβ σα = εαβγ σγ (D) σα σβ + σβ σα = 2 δαβ...
H is the Hamiltonian, L⃗ the orbital angular momentum and Lz is the z-component of L⃗ . The 1s state of the hydrogen atom in the non-relativistic formalism is an eigen function of ...
An atom with non-zero magnetic moment has an angular momentum of magnitude √12 \hbar. When a beam of such atoms is passed through a Stern - Gerlach apparatus, how many beams does i...
In the vector model of angular momentum applied to atoms, what is the minimum angle in degrees (in integer) made by the orbital angular moment um vector and the positive z axis for...
The mean distance between the two atoms of HD molecule is r, where H and D denote hydrogen and deuterium, respectively . The mass of the hydrogen atom is mH. The energy difference ...
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 int...
The Δ+ baryon with spin 3 2, at rest, decays to a proton and a pion (Δ+ → p + 𝜋0). The Δ+ has positive intrinsic parity and 𝜋0 has negative intrinsic parity. The orbital angular ...
Consider an electron in the energy eigenstate 𝜓211(r ) of the hydrogen atom. Given that the radial probability distribution of the electron in such a state takes its maximum value...
Consider two particles with angular momenta j1 = 2\hbar and j2 = \hbar/2. If the expression |j = 5/2,m = 3/2⟩ = {c1|j1 = 2, m1 = 1⟩|j2 = 1/2, m2 = 1/2⟩ + c2|j1 = 2, m1 = 2⟩|j2 = 1/...