Atomic number of Hydrogen like species that has a wave length difference of 59.3 nm between first lin e of Balmer and first line of Lyman series is (R H = 109678 cm − 1 )

Step-by-step solution

Wavelength of 1st line in Balmer series, 1 λ B = Z 2 R H 1 2 2 − 1 3 2 = 5 36 R H Z 2 or λ B = 36 5 R H Z 2 Wavelength of 1st line in Lyman series is, 1 λ L = Z 2 R H 1 1 2 − 1 2 2 or λ L = 4 3 × R H Z 2 Difference λ B − λ L = 59.3 × 10 − 7 = 36 5 R H Z 2 − 4 3 R H Z 2 = 1 R H Z 2 36 5 − 4 3 Z 2 = 88 59.3 × 10 − 7 × 109678 × 15 = 9.0 or Z = 3 Hydrogen-like species is Li 2+