Question

If in H-atom for any transition, it produce wavelength of 100 nm, then what will be wavelength of same transition in He+ atom?

Answer 1

For H-atom 

\(\frac{1}{\lambda _H} = R_H\left[\frac{1}{(n_1^2) } - \frac{1}{(n_2^2)}\right]\ ..(i)\)

For He⁺ atom 

\(\frac{1}{\lambda_{He^+}} = R_H.Z^2\ [\frac{1}{(n_1^2)} - \frac{1}{(n_2^2)}]\ ...(ii)\) 

In equation (1) and (2)

\(\lambda_{He^+} = \frac{\lambda _H}{Z^2} = \frac{100}{(2)^2} = \frac{100}{4} = 25\ nm\)