Question

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

Options

• 2πa₀

• 4πa₀

• 6πa₀

• 8πa₀

Answer 1

The de Broglie wavelength of an electron in the 4^th Bohr orbit is 8πa₀.

Explanation:

2πr = nλ

r = ${\displaystyle \frac{{\text{n}}^2{\text{a}}_0}{\text{Z}}}$

${\displaystyle 2\pi \times \frac{4^2}{1}{\text{a}}_0}$ = 4λ

⇒ λ = ${\displaystyle 2\pi \times \frac{4}{1}{\text{a}}_0}$

⇒ λ = 8πa₀