Question

A gas absorbs a photon of 355 nm and emits two wavelengths. If one of the emission is at 680 nm, the other is at:

• A. 518 nm
• B. 1035 nm
• C. 325 nm
• D. 743 nm

Answer 1

The correct option is D

743 nm

As we know, $c=\nu \lambda$ $\Rightarrow \nu =\frac{c}{\lambda }$

By Planck's theory,

$E=h\nu \Rightarrow E=\frac{hc}{\lambda }$

Now, using the law of conservation of energy: Absorbed Energy = Emitted Energy

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

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

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

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