The question is incomplete, the complete question is;
Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc) where the light is found.
(a) n=2 → n=1
(b) n=3 → n=1
(c) n=4 → n=2
(d) n=5 → n=2
Answer:
see explanation
Step-by-step explanation:
From;
ΔE = -2.18 * 10^-18 J (1/nf^2 - 1/ni^2)
a)
-2.18 * 10^-18 J (1/1^2 - 1/2^2)
= -2.18 * 10^-18 J *3/4
=- 1.64 * 10^-18 J
obtain wavelength from;
λ = hc/E
h= 6.6 * 10^-34Js
c= 3 *10^8 m/s
λ = 6.6 * 10^-34 * 3 *10^8 /1.64 * 10^-18
λ = 12.1* 10^-8 m
This belongs to the ultraviolet region
b)-2.18 * 10^-18 J (1/1^2 - 1/3^2)
= -2.18 * 10^-18 J *8/9
=- 1.94 * 10^-18 J
obtain wavelength from;
λ = hc/E
h= 6.6 * 10^-34Js
c= 3 *10^8 m/s
λ = 6.6 * 10^-34 * 3 *10^8 /1.94 * 10^-18
λ = 10.2 * 10^-8 m
This belongs to the ultraviolet region
c)-2.18 * 10^-18 J (1/2^2 - 1/4^2)
= -2.18 * 10^-18 J *3/16
=- 4.1 * 10^-19 J
obtain wavelength from;
λ = hc/E
h= 6.6 * 10^-34Js
c= 3 *10^8 m/s
λ = 6.6 * 10^-34 * 3 *10^8 /4.1 * 10^-19
λ = 4.83* 10^-7 m
This belongs to the visible region
d) -2.18 * 10^-18 J (1/2^2 - 1/5^2)
= -2.18 * 10^-18 J *21/100
=- 4.58 * 10^-19 J
obtain wavelength from;
λ = hc/E
h= 6.6 * 10^-34Js
c= 3 *10^8 m/s
λ = 6.6 * 10^-34 * 3 *10^8 /4.58 * 10^-19
λ = 4.32* 10^-7 m
This belongs to the visible region