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

1 Answer
Jun 14, 2018

Answer:

#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#