GATE CY 2020 Question Paper (01-Feb-2020) (Shift 2)

Consider that AgX crystallizes in rock salt structure. The density of AgX is 6477 kg/m³ and unit cell length is 577.5 pm. Atomic weight of Ag is 107.87 g mol⁻¹. The atomic weight of X (in g mol⁻¹, rounded off to two decimal places) is ______

The total number of g) lines expected in the EPR spectrum of a solution of bis(salicylaldimine) copper(II) having pure ⁶³Cu and ¹⁴N at 77 K is ______

(Given: I values of ⁶³Cu, ¹⁴N and ¹H are $\frac{3}{2}$, 1 and $\frac{1}{2}$, respectively)

Among the following,

[B12H12]²⁻, [NI5(CO)12]²⁻, [C2B9H11]²⁻, RH6(CO)16, Os5(CO)20, B5H11, B6H10

the total number of species having nido structure is ______

(Given: atomic numbers of H, B, C, O, Ni, Rh and Os are 1, 5, 6, 8, 28, 45 and 76, respectively)

The frequency (in cm⁻¹, rounded off to two decimal places) for pure rotational line in the spectrum of NO molecule due to change in the quantum number from J = 1 to J = 2 is ______

(Given: Moment of inertia of NO = 1.6427 × 10⁻⁴⁶ kg m²; h = 6.626 × 10⁻³⁴ J s; c = 3 × 10⁸ m/s)

The % error (rounded off to two decimal places) in the ground state energy of a particle in a one dimensional box of length ‘a’ described by a trial variation function ϕ = x(a - x), where 0 ≤ x ≤ a, is ______

(Given: The true ground state energy of the above system is h²/ 8ma²; ${\int }_0^a{\varphi }^{\ast }\varphi d\tau =a^5/30$)