Answer: The longest wavelength of light that will produce free chlorine atoms in solution is 493 nm.
Explanation:
[tex]Cl_2\overset{h\nu}\rightarrow Cl^-,Delta H_{rxn}=242.8kJ/mol[/tex]
Energy required to produce free chlorine atoms from one mole of chlorine gas :
= 242.8kJ = [tex]242.8\times 1000=242800 Joules[/tex] (1kJ=1000J)
1 mole = [tex]6.022\times 10^{23}[/tex] molecules
For [tex]6.022\times 10^{23}[/tex] molecules = 242,800 Joules
For one molecule of chlorine gas = [tex]\frac{242800 Joules/mol}{6.022\times 10^{23} mol^{-1}}=40,318.83\times 10^{-23}Joules[/tex]
According to photoelectric equation:
[tex]E=h\nu=\frac{hc}{\Lambda }[/tex]
E = Energy of the photon of light used to produce free chlorine atoms
[tex]\nu[/tex]= frequency of the light used to produce free chlorine atoms
h = Planck's constant =[tex]6.626\times 10^{-34}J.s[/tex], c = speed of light=[tex]3\times 10^8 m/s[/tex]
[tex]\lambda [/tex] = wavelength of the light used to produce free chlorine atoms
[tex] 40,318.83\times 10^{-23}J=\frac{hc}{\Lambda }=\frac{6.626\times 10^{-34} J.s\times 3\times 10^8 m/s}{\lambda }[/tex]
[tex]\lambda=0.0004930203\times 10^{-3} m=493.0203\times 10^{-9} m=493 nm[/tex]
The longest wavelength of light that will produce free chlorine atoms in solution is 493 nm.
