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

Answer:

a) 1.2*10^-7 m

b) 1.0*10^-7 m

c) 9.7*10^-8 m

d) ultraviolet region

Explanation:

To find the different wavelengths you use the following formula:

$\frac{1}{\lambda}=R_H(1-\frac{1}{n^2})$

RH: Rydberg constant = 1.097 x 10^7 m^−1.

(a) n=2

$\frac{1}{\lambda}=(1.097*10^7m^{-1})(1-\frac{1}{(2)^2})=8227500m^{-1}\\\\\lambda=1.2*10^{-7}m$

(b)

$\frac{1}{\lambda}=(1.097*10^7m^{-1})(1-\frac{1}{(3)^2})=9751111,1m^{-1}\\\\\lambda=1.0*10^{-7}m$

(c)

$\frac{1}{\lambda}=(1.097*10^7m^{-1})(1-\frac{1}{(4)^2})=10284375m^{-1}\\\\\lambda=9.7*10^{-8}m$

(d) The three lines belong to the ultraviolet region.