GATE CY 2022 Question Paper (06-Feb-2022) (Shift 2)

The parameter(s) fixed for each system in a canonical ensemble is(are)

The CORRECT statement(s) about the spectral line broadening in atomic spectra is(are)

The number of peaks exhibited by T in its broadband proton decoupled ¹³C NMR spectrum recorded at 25 °C in CDCl₃ is

The diffraction angle (in degree, rounded off to one decimal place) of (321) sets of plane of a metal with atomic radius 0.125 nm, and adopting BCC structure is

(Given: the order of reflection is 1 and the wavelength of X-ray is 0.0771 nm)

For the angular momentum operator L̂ and the spherical harmonics ${\mathrm{Y}}_{\mathrm{lm}}(\theta ,\varphi ),({\hat{\mathrm{L}}}_{\mathrm{x}}^2+{\hat{\mathrm{L}}}_{\mathrm{y}}^2){\mathrm{Y}}_{21}(\theta ,\varphi )=\mathrm{n}{\mathrm{\hslash }}^2{\mathrm{Y}}_{21}(\theta ,\varphi )$.

The value of 𝑛 is