Given that diatomic chlorine is the most stable form of the element, and that the ΔHf° value for atomic chlorine is +121.7 kJ/mol, calculate the maximum wavelength that can dissociate diatomic chlorine into monoatomic chlorine. What type of radiation (UV-A, UV-B, UV-C) does this wavelength correspond to?

The maximum wavelength of light that can dissociate diatomic chlorine into the monatomic chlorine form is 984 nm.

Explanation:

Given: ΔHf° value for atomic chlorine is +121.7 kJ/mol

1 Step

Converting kJ/mol into kJ (knowing that in 1 mol there is 6.023*10^23 molecules)  

ΔHf° in kJ = 121.7 kJ/mol* 1 mole / 6.023*10^23

ΔHf° = 2.02*10^-22 kJ

ΔHf° = E = 2.02*10^-19 J

2 Step

Converting ΔHf° to a wavelength:

knowing the E = h*C/У

h = 6.626 x 10^-34 J·s

C = 3.00 x 10^8 m/s

У = h*C/E = (6.63 x 10^-34 J·s)(3.00 x 108 m/s) / 2.02*10^-19 J

У = 9.84*10^-7 m = 984 nm

3 Step (What type of radiation?)

UV-A wavelength range = 315 nm to 400 nm

UV-B wavelength range = 280 nm to 315 nm

UV-C wavelength range = 100 nm to 280 nm

This wavelength is not corresponding to any of the wavelength range (UV-A, UV-B, UV-C).