Question

The Lyman series comprises a set of spectral lines. All of these lines involve a hydrogen atom whose electron undergoes a change in energy level, either beginning at the n = 1 level (in the case of an absorption line) or ending there (an emission line).

The inverse wavelengths for the Lyman series in hydrogen are given by:
1/λ = RH (1 - 1/n^2) ,
where n = 2, 3, 4, and the Rydberg constant RH = 1.097 x 10^7 m^−1. (Round your answers to at least one decimal place. Enter your answers in nm.)
(a) Compute the wavelength for the first line in this series (the line corresponding to n = 2).
(b) Compute the wavelength for the second line in this series (the line corresponding to n = 3).
(c) Compute the wavelength for the third line in this series (the line corresponding to n = 4).
(d) In which part of the electromagnetic spectrum do these three lines reside?
O visible light region
O infrared region
O ultraviolet region
O gamma ray region
O x-ray region

Answer 1

The wavelength for the first line in the Lyman series is 1.213 nm, the wavelength for the second line is 1.033 nm, and the wavelength for the third line is 0.979 nm. These lines reside in the ultraviolet region of the electromagnetic spectrum.

Step-by-step explanation:

The wavelength for the first line in the Lyman series (the line corresponding to n = 2) can be calculated using the formula 1/λ = RH (1 - 1/n^2), where RH is the Rydberg constant and n is the energy level. Plugging in the values, we get:

The wavelength for the second line in the Lyman series (the line corresponding to n = 3) can be calculated as:

The wavelength for the third line in the Lyman series (the line corresponding to n = 4) can be calculated as:

These three lines of the Lyman series reside in the ultraviolet region of the electromagnetic spectrum.