Question

Sun glasses have small amount of $AgCl$ incorporated in the lenses. When light of appropriate wavelength is exposed it turns to gray colour to reduce the glare following the reactions:
$AgCl\stackrel{hv}{\to }Ag\left(\text{Gray}\right)+\frac{1}{2}C{l}_2$

If the heat of reaction for the decomposition of $AgCl$ is $248{\text{kJ mol}}^{-1}$. Find the wavelength needed to induce the desired process?

• A. $4.83\times {10}^{-7}\text{m}$
• B. $9.66\times {10}^{-7}\text{m}$
• C. $2.41\times {10}^{-7}\text{m}$
• D. $4.83\times {10}^{-6}\text{m}$

Answer 1

The correct option is A $4.83\times {10}^{-7}\text{m}$

Heat of reaction for decomposition $=248\times {10}^3{\text{J mol}}^{-1}$ = Energy of 1 mole of photons
According to Planck's theory, E = $nhv$
where n is number of photons,
Therefore,
$n\times \frac{hc}{\lambda }=248\times {10}^3$

$\Rightarrow \lambda =\frac{6.626\times {10}^{-34}\times 3\times {10}^8\times 6.023\times {10}^{23}}{248\times {10}^3}$ $\lambda$ $=4.83\times {10}^{-7}\text{m}$