Introduction:
Photochemical dissociation is the process in which a molecule is dissociated into its constituent atoms when exposed to radiation. In the case of chlorine (Cl2) molecules, photochemical dissociation can occur when it absorbs certain wavelengths of radiation. The wavelength of the radiation required for the dissociation can be calculated using the bond dissociation energy of the Cl-Cl bond.

Calculation:
The bond dissociation energy (BDE) of the Cl-Cl bond is given as 241 kJ/mol. This value represents the energy required to break one mole of Cl-Cl bonds. To calculate the wavelength of the radiation that causes dissociation, we can use the relationship between energy and wavelength.

1. Convert BDE to energy per molecule:
- Divide the BDE (241 kJ/mol) by Avogadro's number (6.022 x 10^23) to obtain the energy per molecule.
- 241 kJ/mol / (6.022 x 10^23) = X kJ/molecule (where X is the energy per molecule)

2. Convert energy to joules:
- Multiply the energy per molecule (X kJ/molecule) by 1000 to convert it to joules.
- X kJ/molecule * 1000 = Y J/molecule (where Y is the energy per molecule in joules)

3. Calculate the frequency of the radiation:
- Use the equation E = h * f, where E is the energy per molecule in joules, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the radiation.
- Y J/molecule = (6.626 x 10^-34 J·s) * f
- Solve for f: f = Y J/molecule / (6.626 x 10^-34 J·s)

4. Calculate the wavelength:
- Use the equation c = λ * f, where c is the speed of light (3.0 x 10^8 m/s), λ is the wavelength, and f is the frequency of the radiation.
- Rearrange the equation to solve for λ: λ = c / f

Result:
By substituting the calculated value of f into the equation for wavelength, we can determine the wavelength of the radiation required for the photochemical dissociation of a chlorine molecule.