The wavelength of the first line of Lyman series for H - atom is equal to that of the second line of Balmer series for a H -like ion. The atomic number Z of H -like ion is

Step-by-step solution

Lyman series of H -atom, we can write h c =R h c ( 1 1^2 - 1 2^2 ) where, symbols have their usual meaning and for second line of Balmer series of H -like ion h c =Z^2 R h c ( 1 2^2 - 1 4^2 ) . Therefore, ( 1 1^2 - 1 2^2 )=Z^2 ( 1 4 - 1 16 ) aligned (1- 1 4 ) & =Z^2 ( 1 4 - 1 16 ) Z & =2.19 2 aligned The approximately value of Z will be 2 .