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

Step-by-step solution

Lyman series for H -ion h c =R h c ( 1 1^2 - 1 2^2 ) And for H-like ion aligned h c & =Z^2 R h c ( 1 2^2 - 1 4^2 ) ( 1 1^2 - 1 2^2 ) & =Z^2 ( 1 4 - 1 16 ) (1- 1 4 ) & =Z^2 ( 1 4 - 1 16 ) Z & =2 aligned