Question

If the radius of Bohr's orbit is x, then de Broglie wavelength of the electron in 3rd orbit is nearly?

Answer 1

`λ ≈19x`

Explanation:

According to de Broglie, the circumference of a stationary orbit must be an integral number of wavelengths

`nλ = 2πr`

Recall that for a hydrogen atom,

`r = n^2a_0`

Then

`nλ = 2πn^2a_0`

`color(blue)(bar(ul(|color(white)(a/a)λ = 2πna_0color(white)(a/a)|)))" "`

If `n = 3` and `"a_0 = x`,

`λ = 2π × 3x = 6πx ≈ 19x`