If a electron is moving around a nucleus of charge 2e in a circular orbit of radius 10^-10 m ,then - Physics - Atoms

Question

If a electron is moving around a nucleus of charge 2e in a
circular orbit of radius 10^-10 m ,then calculate the intial
frequency of light emitted by the electron

Jyoti Pant · Accepted Answer

The centripetal force for the circular motion of the electron is provided by the coulomb attraction of the nucleus.
If v=speed of the electron and r=radius of the circular path,then

$\frac{m v^{2}}{r} = \frac{2 e^{2}}{4 π \in_{0} r^{2}} o r v = [{\frac{2 e^{2}}{4 π \in_{0} m r}]}^{1 / 2} N o w f r e q u e n c y ν = \frac{2 π r}{v} = \frac{2 π r}{[{\frac{2 e^{2}}{4 π \in_{0} m r}]}^{1 / 2}} I n i t i a l f r e q u e n c y = \frac{1.414 \times \sqrt{9 \times 10^{9}} \times 1.6 \times 10^{- 19}}{\sqrt{9.1 \times 10^{- 31}} \times 2 \times 3.14 \times {{(10}^{- 10})}^{3 / 2}}$

=3.6 x $10^{15} H z$

If a electron is moving around a nucleus of charge 2e in a circular orbit of radius 10^-10 m ,then calculate the intial frequency of light emitted by the electron.