The ratio of the speed of the electron in the ground state of hydrogen atom to the speed of light is

The ratio of the speed of an electron in the ground state of H atom to speed of light is 1/137.

Explanation:

Speed of electron in the nth orbit for the hydrogen atom is given as:

\(v=\frac{e^{2}}{2\epsilon _{0}nh}\)

The value of n in the ground state is 1.

Substituting the same in the above equation, we get

\(v=\frac{e^{2}}{2\epsilon _{0}h}\) \(\frac{v}{c}=\frac{e^{2}}{2\epsilon _{0}ch}\) \(\frac{v}{c}=\frac{(1.6\times 10^{-19})^{2}}{2\times 8.85\times 10^{-12}\times 3\times 10^{8}\times 6.6\times 10^{-34}}\) \(\frac{v}{c}=\frac{1}{137}\)

Was this answer helpful?

 
   

3 (5)

(5)
(4)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question