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Certain sunglasses have small crystals of $\ce{AgCl}$ incorporated into the lenses, on exposure to light of appropriate wavelength produces a grey colour to reduce the glare following the reaction: $$\ce{ \underset{(colourless)}{AgCl} ->[h\nu] \underset{(grey)}{Ag} + Cl }$$

If the heat of reaction for the decomposition of $\ce{AgCl}$ is $\pu{248 kJ/mol}$, what maximum wavelength is needed to induce the desired process?

Does this mean that by absorbing only a certain wavelength, electrons move for a lower to higher energy state and react? Why does it only emit grey light, but does not any colours of the spectrum in order?

The question asks about the "heat of decomposition". Does this mean the energy required to excite an electron and cause a reaction? When a molecule absorb a photon, it is breaking the atoms apart by moving electrons?

Please help clear up any misunderstandings in this question.

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    $\begingroup$ HINT "Heat" is just energy... $\endgroup$ – MaxW Dec 31 '20 at 21:10
  • $\begingroup$ Does this answer your question? Why is the dissolution of AgCl considered endothermic? $\endgroup$ – cngzz1 Jan 1 at 7:19
  • $\begingroup$ This has nothing to do with sunglasses: that is the irrelevant pseudo-pretext stuff. The question is this: “What wavelength of light, in nm units, is such that a mole of photons of that wavelength would have a total energy of 248 kJ?” $\endgroup$ – Ed V Jan 2 at 15:37
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The intent of the question is that the reaction: $$ \ce{Ag+} + \ce{Cl-} \rightarrow \ce{Ag} + \ce{Cl}$$ requires absorbing exactly one photon. That photon must have at least the energy required to perform this reaction. The grey colour produced is caused by the metallic silver ($\ce{Ag^0}$) formed by the reaction.

Because a photon's energy is inversely proportional to its wavelength, $E_{photon}=\frac{h c}{\lambda}$, in order to have the required energy or more to cause the reaction, the photon must have a required wavelength or less. So there is a maximum wavelength that the photon may have in order to cause this reaction.

You're told that the energy required to decompose 1 mole of $\ce{AgCl}$ is 248 kJ/mol, so you have to figure out the energy per atom/photon and convert that energy to a wavelength.

This is an example of the photoelectric effect - that light comes in quantised particles (set amounts of energy) called photons, and certain processes require absorbing a single photon at a time with enough energy, rather than absorbing more lower energy light over time, as if the light was only a continuous wave.

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