Question

An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 700 nm. Find the net energy absorbed by the atom in the process.

Answer 1

Given:
Wavelength of absorbed photon, ${\lambda }_1$ = 500 nm
Wavelength of emitted photon, ${\lambda }_2$ = 700 nm
Speed of light, c = 3$\times {10}^8$ m/s
Planck's constant, h = 6.63$\times$10^$-34$ Js
Energy of absorbed photon,
$E_1=\frac{hc}{{\lambda }_1}=\frac{h\times 3\times {10}^8}{500\times {10}^{-9}}$
Energy of emitted photon,
$E_2=\frac{hc}{{\lambda }_2}=\frac{h\times 3\times {10}^8}{700\times {10}^{-9}}$
Energy absorbed by the atom in the process:
$$\begin{gathered} E_1-E_2=hc\left[\frac{1}{{\lambda }_1}-\frac{1}{{\lambda }_2}\right] \\ =6.63\times 3\left[\frac{1}{5}-\frac{1}{7}\right]\times {10}^{-19} \\ =6.63\times 3\times \frac{2}{35}\times {10}^{-19} \\ =1.136\times {10}^{-19}\mathrm{J} \end{gathered}$$