Question:
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
Answer:
For ground level (n1)=1
Energy of the ground level
E1= -13.6/ n12 = -13.6/1 = -13.6 eV
For higher level (n2)=4
Energy of the ground level
E2= -13.6/ n22 = -13.6/(4)2 = -13.6/16 = -0.85 eV
The energy absorbed by a photon,
E = E1 - E2
= -0.85 - (-13.6)
= -0.85 +13.6
= 12.75 eV
= 12.75 x 1.6 x 10-19
= 20.4 x 10-19
= 2.04 x 10-18 J
For, a photon of a wavelength
E=hc/λ Where, h= 6.6 x x 10-34 J, C = speed of light = 3 x x 108 m/s
Therefore,
E=hc/λ
λ = hc/E
= 6.6 x x 10-34 x 3 x 108/2.04 x 10-18
= 9.7 x 10-8 m
= 97 nm
Frequency
v=c/λ
= 3 x 108/9.7 x 10-8
= 3.1 x 1015 Hz
Hence, wavelength of photon is 97 nm and frequency is 3.1 x 1015 Hz
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