Final answer:
The maximum wavelength of light capable of dissociating the Br-I bond in iodine monobromide with a bond energy of 179 kJ/mol is approximately 668 nm. This calculation is done using Planck's equation.
Step-by-step explanation:
To calculate the maximum wavelength of light capable of dissociating the Br-I bond in iodine monobromide where the bond energy is 179 kJ/mol, we will use Planck's equation that relates energy (E) to wavelength (λ) given as E = hc/λ, where h is Planck's constant (6.626 x 10-34 J·s) and c is the speed of light (3.00 x 108 m/s). First, we need to convert the bond energy to joules per molecule by dividing by Avogadro's number (6.022 x 1023 mol-1):
Bond energy in J/molecule = (179 x 103 J/mol) / (6.022 x 1023 mol-1) = 2.971 x 10-19 J/molecule
Now, using the equation E = hc/λ, rearrange to solve for λ:
λ = hc/E = (6.626 x 10-34 J·s × 3.00 x 108 m/s) / (2.971 x 10-19 J/molecule)
Calculating this gives a maximum wavelength (λ) which is:
λ = (6.626 x 10-34 × 3.00 x 108) / 2.971 x 10-19 ≈ 6.68 x 10-7 meters or 668 nm
Therefore, the maximum wavelength of light capable of dissociating the Br-I bond in iodine monobromide is approximately 668 nm.