The electron revolving in the n-th orbit of `Be^(3+)` ion has the same speed as that of the electron in the ground state of hydrogen atom. Find the value of n.

Explanation

Velocity of electron in the n-th orbit of hydrogen-like species is given by, `v_(n)=(Z)/(n)xxv_(1)`
[where `v_(1)`=velocity of electron in the 1st orbit of H-atom and Z=atomic number of hydrogen like species].
now for `Be^(3+)` ionk `Z=4`, so `v_(n)=(4)/(n)xxv_(1)`
But it is given that, `v_(n)=v_(1)`
`therefore v_(1)=(4)/(n)v_(1) or n=4`.