Question

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

• A. $5\lambda$
• B. $6\lambda$
• C. $7\lambda$
• D. $8\lambda$

Answer 1

The correct option is B $6\lambda$

$mvr=\frac{nh}{2\pi }$
$r=\frac{n}{2\pi }\left(\frac{h}{mv}\right)$
$r=\frac{n}{2\pi }\left(\lambda \right)(n=6)$
Circumference $=2\pi r$
$=2\pi \left(\frac{3\lambda }{\pi }\right)=6\lambda$