Question

Photography lenses incorporate small accounts of silver chloride in the glass of the lines. When light hits the Agcl particles, the following reaction occurs:

$Agcl\stackrel{hv}{\to }Ag+cl$

The silver metal formed causes the lenses to darken. The enthalpy change for this reaction is $3.10\times {10}^2$KJ mol.Assuming that all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction.

Short answer

The maximum wavelength of light that can cause this reaction is 386 nm$386nm$.

Step-by-step solution

Step-by-step-solution

[First, we determine the energy of light for the atom (E)]

The energy of light,$$\begin{gathered} ∆H=3.10\times {10}^{2}KJ/mol \\ =3.10\times {10}^{5}J/mol \\ E=\frac{∆H}{N_A} \\ =\frac{3.10\times {10}^{5}J}{6.022\times {10}^{23}} \end{gathered}$$

(Now, we can calculate the maximum wavelength of light for this reaction)

Speed of light, $c=2.998\times {10}^{-8}m/s$

Plank’s constant, $h=6.626\times {10}^{-34}J/s$

localid="1664338177024" $$\begin{gathered} h\frac{6.626\times {10}^{-34}J/s\times 2.998\times {10}^{-8}m/s}{{\displaystyle \frac{3.10\times {10}^{5J}}{6.022\times {10}^{23}}}} \\ h=3.86\times {10}^{-7}m \\ h=386nm \end{gathered}$$