The wavelength of the first line of the Lyman series for a hydrogen atom is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number Z of the hydrogen-like ion is
Step 1: Given data
For the first line of the Lyman series, let the wavelength be
For the second line of the Balmer series, let the wavelength be
Given
Step 2: Formula used
Electron jumps from to to produce the first line of the Lyman series, therefore
, Here R is rydberg constant
Electron jumps from to to produce the second line of the Balmer series, therefore
, Here R is rydberg constant
Step 3: Calculating the atomic number of hydrogen-like ion
Hence, option D is the correct answer.