In H-atom if `r1` is the radius fo first Bohr orbit de-Broglie wavelength of an elecrton in ` 3^(rd)` orbit is :

Options

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

Answer

B

Explanation

(b) `r_n = (n^2 a_0)/(Z)`, `therefore r_0 prop n_2`
`(r_3)/(r_1) = (9)/(1)`
`r_3 = 9 r_1 = 9 x`
Also `mvr_n = (nh)/(2 pi)`
`mvr_3 = (3h)/(2 pi)`
`mv = (h)/( 6 pi x)`
`lamda = (h)/(mv) = 6 pi x`.