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.

For a hydrogen -like particle, derive the expression : v_(n) = ((Ze^(2

1.	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.
Answer» Solution :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)`