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

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Answer 1 · 2018-06-14T00:10:00

$λ ≈19x$

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 $"a_0 = x$ ,

$λ = 2π × 3x = 6πx ≈ 19x$