JEE Advanced2021PhysicsAtomic PhysicsActual
Which of the following statement(s) is (are) correct about the spectrum of hydrogen atom?
Options
- AThe ratio of the longest wavelength to the shortest wavelength in Balmer series is 9 5 .
- BThere is an overlap between the wavelength ranges of Balmer and Paschen series.
- CThe wavelengths of Lyman series are given by 1 + 1 m 2 λ 0 , where λ 0 is the shortest wavelength of
- DThe wavelength ranges of Lyman and Balmer series do not overlap.
Correct answer
A. The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9 5 .
Step-by-step solution
For Balmer Series: Shortest wavelength, E o 4 = h c λ s Longest wavelength, E o 4 − E 0 9 = h c λ l = 5 E o 36 ∴   λ l λ s = 9 5 Range of energy level in Balmer series, 5 E 0 36 ,   E 0 4 Range of energy level in Paschen series, 7 E 0 144 ,   E 0 9 Hence, no overlap. For Lyman series: For shortest wavelength, E 0 = h c λ 0 For general wavelength, E 0 - E 0 n 2 = h c λ ⇒ 1 1 − 1 n 2 = λ λ 0 ∴   λ = n 2 n 2 − 1 λ