Question

The de-Broglie wavelength of an electron in 4^th orbit is ______.

(r = radius of 1^st orbit)

Options

• 2πr

• 4πr

• 8πr

• 16πr

Answer 1

The de-Broglie wavelength of an electron in 4^th orbit is 8πr.

Explanation:

de-Broglie wavelength, `lambda="h"/"P"`        ...(i)

According to Bohr's quantisation condition

`"mvr"_"n"="nh"/(2pi)`

`"pr"_"n"="nh"/(2pi)`      ...(ii)

From Eqs (i) and (ii), we get

`lambda=("h"xx2pir_"n")/"nh"=(2pir_"n")/"n"`

For fourth orbit (n = 4),

`lambda=(2pir_4)/4`    ...(iii)

Moreover, r ∝ n²

`=>r_1/r_4=1^2/4^2=>r_4=16r_1`

Substituting the value of r₄ in Eq. (iii), we get

`lambda(2pi[16r_1])/4=8pir_1=8pir`