The amount of energy necessary to break a chemical bond between A and B AB is known as bond dissociation energy. The amount of the bond established between atoms A and B determines the bond dissociation energy. The following information has been provided:
242 KJ mol-1 is the amount of energy required to break one mole of chlorine.
The longest wavelength of light capable of breaking a single Cl-Cl bond is what we’re looking for. We already know that the energy of radiation is proportional to its wavelengths. The relationship is stated as follows:
E = hυ = hCλ
However, we have considered the bond dissociation energy for the one-mole chlorine molecule.
Thus the number of chlorine molecules in one mole is always equal to Avogadro’s number NA = 6.023 × 1023 mol−1
Thus the energy relation is modified as, E = NAhC/λ (1)
Where E is the bond dissociation energy, NA is the Avogadro’s number, h is the Planck’s constant 6.626 × 10−34 J s−1 , c is the speed of light 3×108 ms−1 and λ is the wavelength of radiation required to break the bond.
Let’s substitute the values in the equation (1), we have 242 KJ mol−1 = (6.023 ×1023 mol−1)(6.626×10−34 Js−1) (3×108 m s−1)/λ
Rearrange equation with respect to wavelength. We have, λ = (6.023 ×1023 mol−1)(6.626×10−34 Js−1) (3×108 m s−1)/242 ×103 mol−1
⇒ λ = (1.19×10−1)/242 ×103J ⇒ λ = 4.94 × 10−7m
The obtained value of the wavelength can be converted into nanometres.
The relation between the one nanometre with the meter is, 1 nm = 10−9 nm
Therefore, λ = 494 × 10−9m = 494 nm
Thus, the longest wavelength required to break a single Cl−Cl is equal to 494 nm .