Question

the wave length of the first line of the Lyman series of hydrogen is identical to the second line of the Balmer series for some hydrogen like ion 'X'.Identify the ion.

Answer 1

1/wavelegth = RZ^2(1/1^2 - 1/2^2) is the first line of the Lyman series.

1/wavelength = RZ^2(1/2^2 - 1/4^2) is the second line of the Balmer series.

You know R and Z for H, solve for wavelength. Plug this wavelength into the Balmer series and solve for Z. Identify the element ion from that.