Question

A dye absorbs a photon of wavelength λ and re-emits the same energy into two photons of wavelength ${\lambda }_1$ and ${\lambda }_2$ respectively. The wavelength λ is related with ${\lambda }_1$ and ${\lambda }_2$ as:

• A. $\lambda =\frac{({\lambda }_1+{\lambda }_2)}{\left({\lambda }_1{\lambda }_2\right)}$
• B. $\lambda =\frac{\left({\lambda }_1{\lambda }_2\right)}{({\lambda }_1+{\lambda }_2)}$
• C. $\lambda =\frac{({\lambda }_1^2+{\lambda }_2^2)}{\left({\lambda }_1{\lambda }_2\right)}$
• D. $\lambda =\frac{\left({\lambda }_1^2{\lambda }_2^2\right)}{({\lambda }_1+{\lambda }_2)}$

Answer 1

The correct option is B $\lambda =\frac{\left({\lambda }_1{\lambda }_2\right)}{({\lambda }_1+{\lambda }_2)}$

$(E{)}_{incident}=E_1+E_2$
$hc/\lambda =hc/{\lambda }_1+hc/{\lambda }_2$
$\lambda =\frac{\left({\lambda }_1{\lambda }_2\right)}{({\lambda }_1+{\lambda }_2)}$