The de Broglie wavelength of an electron in the $4^{\text{th}}$ Bohr orbit is:

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Atomic Structure

The de Broglie wavelength of an electron in the

4^{th}

Bohr orbit is:

Answer: (D)

Bohr's condition that the orbit's circumference hold a whole number of de Broglie wavelengths reads

2 π r = nλ

. For hydrogen the

n

th radius is

n^{2} a_{0}

, so the fourth orbit has

r = 16 a_{0}

. Then

λ = \frac{2 π ( 16 a _{0} )}{4} = 8 π a_{0}

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option