Question

A gas absorbs a photon of $355\mathrm{nm}$ and emits it at two wavelengths. If one of the emissions is at $680\mathrm{nm}$, the other is at

• A. $1035\mathrm{nm}$
• B. $325\mathrm{nm}$
• C. $743\mathrm{nm}$
• D. $518\mathrm{nm}$

Answer 1

The correct option is C

$743\mathrm{nm}$

Step 1: Given data

The wavelength of the photon$=355\mathrm{nm}$

The wavelength of one emission$=680\mathrm{nm}$

Step 2: Calculating the other wavelength

According to the formula, Absorbed energy$=$emitted energy

$\Rightarrow \frac{\mathrm{hc}}{\mathrm{\lambda }}=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}+\frac{\mathrm{hc}}{{\mathrm{\lambda }}_2}$

$\Rightarrow \frac{1}{\mathrm{\lambda }}=\frac{1}{{\mathrm{\lambda }}_1}+\frac{1}{{\mathrm{\lambda }}_2}$

$\Rightarrow \frac{1}{355}=\frac{1}{680}+\frac{1}{{\mathrm{\lambda }}_2}$

$\Rightarrow \frac{1}{{\mathrm{\lambda }}_2}=\frac{1}{355}-\frac{1}{680}$

$\Rightarrow \frac{1}{{\mathrm{\lambda }}_2}=\frac{680-355}{355\times 680}$

$\Rightarrow {\mathrm{\lambda }}_2=743\mathrm{nm}$

Final answer: The other wavelength that photon emits$=743\mathrm{nm}$