Question

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. $\frac{4}{\lambda }$

Answer 1

The correct option is C $4\lambda$

An electron is moving in Bohr's fourth orbit. Its de-Broglie wavelength is $\lambda$. The circumference of the fourth orbit is
$4\lambda$

Note: For nth orbital, the circumference is $n\lambda$.

From Bohr's fourth postulate, the angular momentum mur is an integral multiple of $\frac{h}{2\pi }$

mur$=n\times \frac{h}{2\pi }$

Circumference $=2\pi r=n\times \frac{h}{mu}=n\times \lambda$

As n=4

Circumference= 4$\lambda$

Hence, the correct option is $D$