An electron in hydrogen atom first jumps from second excited state to first excited state and then from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be a, b and c respectively, Then

Options

A. `z = 1//x`
B. `x = 9//4`
C. `y = 5//27`
D. `z = 5//27`

Answer

B

Explanation

`E_(1) = (hc)/(lambda) [(1)/(n_(1)^(2)) - (1)/(n_(2)^(2))]`
For second excited state to first excited state
`E_(1) = (hc)/(lambda) [1/4 - 1/9] rArr (hc)/(lambda) ((5)/(36))`
For first excited state to ground excited state
`E_(2) = (hc)/(lambda) [1-(1)/(4)] rArr (hc)/(lambda) [(3)/(4)]`
(A) `(E_(1))/(E_(2)) = (5)/(27)` , (B) `(E_(1))/(E_(2)) = ((hc)/(lambda_(1)))((lambda_(2))/(hc)) = (lambda_(2))/(lambda_(1)) = 27/5`
(C) `P prop 1/(lambda) rArr (P_(1))/(P_(2)) = 5/27`