Question

In third orbit of hydrogen atom wavelength of revolving electron is $\lambda .$ Calculate its circumference.

• A. $\lambda $
• B. $2\lambda $
• C. $3\lambda $
• D. $4\lambda $

Answer 1

Answer: (C)

Wavelength of electron can be calculated as
$\lambda =\frac{h}{p}=\frac{h}{m v}...\left(1\right)$
Also, Angular momentum of electron can be calculated as
$mvr=\frac{n h}{2 \pi }...\left(2\right)$
From first and second equation
$\frac{\lambda }{m v r}=\frac{h \times 2 \pi }{m v \times n h}\frac{\lambda }{r}=\frac{2 \pi }{n}$
$n\lambda =2\pi r$
$3\lambda =2\pi r$
Hence its circumference is $3\lambda $