An electron in the hydrogen atom absorbs energy and jumps to the 4th orbit. It jumps back to the ground state in steps e.g., from 4th to 3rd orbit, then from 3rd to 2nd orbit and finally to the ground state etc.
If `a_(0)` represents Bohr radius, the de-Broglie wavelength of the electron when it moves in the 3rd orbit after absorbing same definite amount of energy will be

Options

A. `a_(0)//3`
B. `9a_(0)`
C. `2pi a_(0)`
D. `6 pi a_(0)`

Answer

D

Explanation

`lamda = (h)/(mv) , mv r = n (h)/(2pi) or (h)/(mv) = (2pi r)/(n)`
`:. lamda = (2pir)/(n)`. But `r_(3) = a_(0) xx 3^(2) = 9 a_(0)`
`:. lamda = (2pi)/(3) xx 9a_(0) = 6pi a_(0)`