We know
[tex]\\ \sf\bull\longmapsto E=hv[/tex]
[tex]\\ \sf\bull\longmapsto v=\dfrac{E}{h}[/tex]
[tex]\\ \sf\bull\longmapsto v=\dfrac{498\times 10^3J}{6.626\times 10^{-34}Js}[/tex]
[tex]\\ \sf\bull\longmapsto v=75.15\times 10^{37}s^{-1}[/tex]
[tex]\\ \sf\bull\longmapsto v=7.5\times 10^{36}s^{-1}[/tex]
Now
[tex]\\ \sf\bull\longmapsto \lambda=\dfrac{C}{V}[/tex]
[tex]\\ \sf\bull\longmapsto \lambda=\dfrac{3\times 10^{8}ms^{-1}}{7.5\times 10^{36}s^{-1}}[/tex]
[tex]\\ \sf\bull\longmapsto \lambda=2.5\times 10^{-28}m[/tex]
The bond energy required to break the oxygen-oxygen double bond is 240 nm
The energy of the incoming photon = [tex]498 * 10^3 J/mol/6.02 * 10^23 moles[/tex] = [tex]8.27 * 10^-19 J[/tex]
Recall that;
E = hc/λ
E = energy of the photon
c = speed of light = [tex]3 * 10^8 m/s[/tex]
λ = wavelength of photon
h = Plank's constant = [tex]6.63 * 10^-34 Js[/tex]
λ = hc/E
λ = [tex]6.63 * 10^-34 * 3 * 10^8/8.27 * 10^-19[/tex]
λ = [tex]2.40 * 10^-7 m[/tex]
λ = 240 nm
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