GATE CY 2019 Question Paper (02-Feb-2019) (Shift 1)

For a bimolecular gas phase reaction P + O → R, the pre-exponential factor is 1 × 10¹³ dm³ mol⁻¹ s⁻¹. The standard entropy of activation at 35°C is _______ JK⁻¹mol⁻¹. (Round off to two decimal points)

(The standard concentration c⁰ = 1 mol dm⁻³; Planck constant h = 6.62 × 10⁻³⁴ J s; Boltzmann constant kB = 1.38 × 10⁻²³ JK⁻¹; Gas constant R = 8.31 J mol⁻¹ K⁻¹)

Character table of point group Ds is given below.Value of (a + b + c + d + e + f + g + h + i + j + k) is equal to _______.

If $\text{⟨}\alpha |{\hat{S}}_x{\hat{S}}_y-{\hat{S}}_y{\hat{S}}_x|\alpha \text{⟩}=i{h}^{2}a$, where ${\hat{S}}_x$ and ${\hat{S}}_y$ are spin angular momentum operators and |α〉 is spin up eigen function, then the value of 'a' is _______. (Round off to one decimal place)

A particle in one dimensional box of length 2a with potential energy

$V=\{\begin{array}{ll}0& |x|<a\\ \infty & |x|>a\end{array}$

is perturbed by the potential V' = cx eV, where c is a constant. The 1${}^{st}$ order correction to the 1${}^{st}$ excited state of the system is _______ × c eV.

Consider a two dimensional harmonic oscillator with angular frequency ωx = 2ω${}_y$ = 6.5 × 10¹⁴rad s⁻¹. The wavelength of x polarized light required for the excitation of a particle from its ground state to the next allowed excited state is _______ × 10⁻⁶ m. (Round off to one decimal place)

(Speed of light c = 3.0 × 10⁸ ms⁻¹)