The ratio maximum wavelength to minimum wavelength in Lyman series is :

Concept:

• The Lyman series is a series of transitions in the hydrogen atom that result in the emission of photons in the ultraviolet part of the electromagnetic spectrum.
• The series is named after the American physicist Theodore Lyman, who first studied it in the early 1900s.

The maximum wavelength in the Lyman series occurs when the electron in the hydrogen atom undergoes a transition from the n = 2 energy level to the n = 1 energy level.

1/λ = R∞ (1/n₁² - 1/n₂²)

1/λ_max = R∞ (1/2² - 1/1²)

Putting R∞ = 1.0973731568539 × 10⁷ m^-1

​λmax = 121.6 nm

Similarly,

The minimum wavelength in the Lyman series occurs when the electron in the hydrogen atom undergoes a transition from the n = infinity energy level to the n = 1 energy level. This transition results in the emission of a photon with a wavelength of 91.2 nm.

• Therefore, the ratio of the maximum wavelength to the minimum wavelength in the Lyman series is:

Maximum wavelength/Minimum wavelength = 121.6 nm/91.2 nm = 1.333...

• So the ratio of the maximum wavelength to the minimum wavelength in the Lyman series is approximately 1.33 = 4/3.

​The correct answer is option (1)