the wavelength of the first line of lyman series for hydrogen atom is equal to that of the second line of balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is

Options

A. 3
B. 4
C. 1
D. 2

Answer

D

Explanation

The wavelength of the first line of lyman series for hydrogen atom is `(1)/(lambda)=R[(1)/(1^2)-(1)/(2^2)]`
The wavelength of the second line of balmer series for hydrogen like ion is `(1)/(lambda')=Z^2R[(1)/(2^2)-(1)/(4^2)]`
According to question, `lambda =lambda`'
`rArrR[(1)/(1^2)-(1)/(2^2)]=Z^2R[(1)/(2^2)-(1)/(4^2)]`or `(3)/(4)=(3Z^2)/(16)` or `Z^2=4` or `Z=2`