Question

The de-Broglie wavelength of an electron in $4^{th}$ orbit of radius r is:

• A. $\frac{\pi r}{2}$
• B. $\frac{\pi r}{4}$
• C. $\pi r$
• D. $4\pi r$

Answer 1

The correct option is A $\frac{\pi r}{2}$

de Broglie wavelength
$\lambda =\frac{h}{p}=\frac{1}{mv}$ ....(1)
Multiply and divide RHS of equation (1) by r
$mvr=\frac{nh}{2\pi }$ ......(2)
$\lambda =\frac{h}{mvr}\times r=\frac{hr}{nh}\times 2\pi =\frac{2\pi r}{n}$ use equation (2)
For $n=4;\lambda =\frac{\pi r}{2}$