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An atom in its ground state is excited when it absorbs a single photon of light. The atom then relaxes back to the ground state by emitting two photons, the first, an orange photon at 600 600 nm, and the second, an infrared photon at 1200 1200 nm. What is the wavelength of the absorbed photon

Answer :

Answer:

400nm

Explanation:

Energy of a photon is inversely proportional to it's wavelength

[tex]E\propto \frac{1}{\lambda}[/tex]   -(1)

Since the energy of the absorbed photon ([tex]E_a[/tex]) is equal to the sum of energies emitted ([tex]E_1+E_2[/tex])

[tex]E_a=E_1+E_2[/tex]

Using the relation of [tex]E[/tex] and [tex]\lambda[/tex],

[tex]\frac{1}{\lambda_a}=\frac{1}{\lambda_1}+\frac{1}{\lambda_2}[/tex]

[tex]\frac{1}{\lambda_a}=\frac{1}{600\times 10^-^9}+\frac{1}{1200\times 10^-^9}[/tex]

[tex]\lambda_a=400\text{nm}[/tex]

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