In a hydrogen atom, an electron is moving in the nth permitted orbit of radius $r_n$. The wavelength associated with this electron is:

$\frac{2πr_n}{n}$

The correct answer is Option (3) → $\frac{2πr_n}{n}$

According to De-Broglie's hypothesis, the wavelength (λ) associated with particle -

$λ=\frac{h}{P}$   [P = momentum]

and,

Bohr model state that the,

$L=nh$

[n = quantum number]

∴ Momentum, $P=\frac{L}{r}=\frac{nh}{r}$

$∴λ=\frac{h}{\frac{nh}{r}}=\frac{2\pi r}{n}$

Now,

$r_n=n^2.r_1$

$∴λ_n=\frac{2πr_n}{n}$