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

The hydrogen-like radial wave function of the 3s orbital is given as

$R_{3,0}=\frac{1}{9\sqrt{3}}{\left(\frac{Z}{a_0}\right)}^{3/2}\left(6-2\rho +\frac{{\rho }^2}{9}\right)e^{-\rho /6}$

where ρ = 2Zr / a₀; Z = atomic number r = distance from the nucleus and a₀ = Bohr radius.

Positions of the radial nodes (in units of a₀) of the 3s orbital are at

$\Delta G_f^0$ and $\Delta H_f^0$ Fe(g) are 370.7 kJ mol⁻¹ and 416.3 kJ mol⁻¹ at 298 K, respectively. Assuming $\Delta H_f^0$ is constant in the interval 250 K to 375. $\Delta G_f^0$ (rounded off to the nearest integer) for Fe(g) at 375 K is:

Adsorption of N₂on TiO₂ was carried out at 75 K. A plot of $\frac{z}{(1-z)V}$ versus z(z = p/p⁰) gives a straight line with an intercept, 4.0 × 10⁻⁶ mm⁻³and slope, 1.0 × 10⁻³ mm⁻³. The volume (rounded off to the nearest integer) corresponding to the monolayer coverage is:

Among the following sets,













the total number of set(s) of diastereomeric pair(s) is ______

Among the following,

















the total number of compounds showing characteristic carbonyl stretching frequency less than 1700 cm⁻¹ in their IR spectra is ______