For a hydrogen -like particle, derive the expression : `v_(n) = ((Ze^(2))/(mr_(n)))^(1//2)` where `v_(n)` is the velocity of the electron at distance `r_(n)` from the nucleus, Z is the atomic number of the H-like particles, m and e are the charge and mass of the electron.

Explanation

For H-like particle, force of attraction between the electron and the nucleus = centrifugal force i.e., `(Ze^(2))/(r_(n)^(2)) = (mv_(n)^(2))/(r_(n)) or v_(n)^(2) = (Ze^(2))/(mr_(n)) or v_(n) = ((Ze^(2))/(mr_(n)))^(1//2)`