An electron in a hydrogen atom undergoes a transition from an orbit with quantum number ni to another with quantum number nf. Vi and Vf are respectively the initial and final potential energies of the electron. If VfVi=6.25, then the smallest possible nf is
Potential energy of a electron in Bohr's modal is given by (assuming Coulombic force) U=−Kze2γ
where, γ= radious
& radius for Bohr's orbital (for mono-electronic system) =0.529n2z
so, UiUr=γ2γ1=n22n21 ...(1)
As, given n2n1=6.25
by comparing above equation to equation (1).
it can be written as,
so the final value of n2=5.