Q. An electron is moving in Bohr’s fourth orbit. Its de-Broglie wavelength is $\lambda$. What is the circumference of the fourth orbit?

A) $\frac{2}{\lambda}$
B) $2\ \lambda$
C) $4\ \lambda$
D) $\frac{4}{\lambda}$
Explanation

(c)
According to Bohr’s concept, an electron always move in the orbit with angular momentum ($mvr$) equal to $nh/2\pi$.
$\therefore mvr = \frac{nh}{2\pi}$
$or\ \ \ \ \ r = \frac{n}{2\pi}.\left( \frac{h}{mv} \right)$
$or\ \ \ \ r = \frac{n\lambda}{2\pi}$
(From de-Broglie equation, $\lambda = \frac{h}{mv}$)
for fourth orbit ($n = 4$)
$r = \frac{2\lambda}{\pi}$
∴ Circumference =$2\pi r = 2\pi \times \frac{2\lambda}{\pi} = 4\lambda$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.