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. J., Tro Nivaldo. Chemistry (p. 346). Pearson Education. Kindle Edition.

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

see explanation

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

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