Question

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 675 nm, and the second, an infrared photon at 1350 nm. What is the wavelength of the absorbed photon?

Answer 1

Answer:

λ=384 nm

Explanation:

Given an atom in normal state absorbed a photon and gone into excited state then again it returns to the normal state by emitting two photons of wavelength 675 nm and 1350 nm

We know that

The energy absorbed = The energy emitted

The energy absorbed / emitted by an atom = $\frac{hc}{z}$

Let z be the wavelength of the recquired photon and $z_{1}$=675 be the wavelength of the first photon and $z_{2}$=1350 be the wavelength of the second photon.

Now

$\frac{hc}{ z} =\frac{hc}{z1} +\frac{hc}{z2}$

$\frac{1}{z} =\frac{1}{z1} +\frac{1}{z2 }$

$\frac{1}{z} =\frac{1}{675} +\frac{1}{1350 }$

$\frac{1}{z} =\frac{1350+675}{1350\times 675}$

$\frac{1}{z} =\frac{2025}{777600}$

z=$\frac{777600}{2025}$

z=384 nm