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, $v=\left(\frac{c}{1}\right)\alpha =\left(3 \times 10^{8}\right)\times \frac{1}{137}=2.2\times 10^{6}ms^{- 1}$
$r=0.53â„«=0.53\times 10^{- 10}m$
Thus, $f=\frac{\left(\right. 2.2 \times 10^{6} m / s \left.\right)}{2 \left(\right. 3.14 \left.\right) \left(\right. 0.53 \times 10^{- 10} m \left.\right)}=6.6\times 10^{15}Hz$