Prove that, velocity of an electron in the first orbit in twice of that revolving in the second orbit of H-atom.

Explanation

The velocity of electron in nth orbit,
`v=(2pie^(2))/(nh)" "[because mvr=(nh)/(2pi) and r=(n^(2)h^(2))/(4pi^(2)me^(2))]`
`therefore`The velocity of electron in first orbit, `v_(1)=(2pie^(2))/(1xxh) and` the velocity of electron in second orbit, `v_(2)=(2pie^(2))/(2xxh)`
Therefore, `(v_(1))/(v_(2))=(2pie^(2))/(h)xx(2h)/(2pie^(2)) =2 or, v_(1)=2v_(2)`.
Hence, the velocity of an electron revolving in the first orbit is twice of that revolving in the second orbit.