Question

Find the frequency of revolution of the electron in the first stationary orbit of $H$ -atom

• A. $6\times 10^{14}Hz$
• B. $6.6\times 10^{10}Hz$
• C. $6.6\times 10^{-10}Hz$
• D. $6.6\times 10^{15}Hz$

Answer 1

Answer: (D)

Let
$T=$ Time period of electron
$r,v,f,c=$ Radius of orbit, speed of electron, frequency of revolution, speed of light ,
$T=\frac{2\pi r}{v},f=\frac{1}{T}=\frac{v}{2\pi r}$
Further, $v=\left(\frac{c}{1}\right)\alpha =\left(3\times 10^8\right)\times \frac{1}{137}=2.2\times 10^{6}m{s}^{-1}$
$r=0.53Å=0.53\times 10^{-10}m$
Thus, $f=\frac{(2.2\times 10^{6}m/s)}{2(3.14)(0.53\times 10^{-10}m)}=6.6\times 10^{15}Hz$