13. A ground state hydrogen atom absorbs a photon of wavelength 94.98 nm and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 4052.3 nm to reach an intermediate level and a second to return to the ground state. What was the wavelength of the second photon emitted?

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valetta valetta · Answer 1 · 2019-10-16T10:33:12+02:00

Answer:

wavelength of the second photon emitted is 97.26 nm

Explanation:

Data provided;

Wavelength absorbed = 94.98 nm

Wavelength of the one of the emitted photon = 4052.3 nm

Now,

The energy is given as:

Energy = [tex]\frac{\textup{hc}}{\lambda}[/tex]

here,

h is the plank's constant

c is the speed of the light

λ is the wavelength

Now,

by the principle of conservation of energy

Initial energy = Final energy

Therefore,

[tex]\frac{\textup{hc}}{94.98}[/tex] = [tex]\frac{\textup{hc}}{4052.3}[/tex] + [tex]\frac{\textup{hc}}{\lambda_1}[/tex]

or

[tex]\frac{\textup{hc}}{\lambda_1}[/tex]= [tex]\frac{\textup{hc}}{94.98}[/tex] - [tex]\frac{\textup{hc}}{4052.3}[/tex]

or

[tex]\frac{\textup{1}}{\lambda_1}[/tex]= [tex]\frac{\textup{1}}{94.98}[/tex] - [tex]\frac{\textup{1}}{4052.3}[/tex]

or

[tex]\frac{\textup{1}}{\lambda_1}[/tex] = 0.0105 - 2.46 × 10⁻⁴

or

[tex]\frac{\textup{1}}{\lambda_1}[/tex] = 0.01028

or

λ₁ = 97.26 nm

Hence,

the wavelength of the second photon emitted is 97.26 nm