The energy required to break one mole of Cl$$-$$Cl bonds in $$\text{Cl}_2$$ is $$242$$ kJ mol$$^{-1}$$. The longest wavelength of light capable of breaking a single Cl$$-$$Cl bond is ($$c = 3 \times 10^8$$ ms$$^{-1}$$ and $$N_A = 6.02 \times 10^{23}$$ mol$$^{-1}$$)

Energy of dissociation is given for one mole of $$Cl-Cl$$ bonds: $$D = 242\text{ kJ mol}^{-1} = 242 \times 10^{3}\text{ J mol}^{-1}$$.

Step 1 - convert this to energy per single bond.
Energy per bond $$E = \dfrac{D}{N_A} = \dfrac{242 \times 10^{3}\ \text{J mol}^{-1}}{6.02 \times 10^{23}\ \text{mol}^{-1}}$$.

Evaluating, $$E \approx 4.02 \times 10^{-19}\text{ J}$$.

Step 2 - relate photon energy to its wavelength.
For one photon, $$E = h c / \lambda$$, where $$h = 6.626 \times 10^{-34}\text{ J s}$$ and $$c = 3.00 \times 10^{8}\text{ m s}^{-1}$$.

Hence $$\lambda = \dfrac{h c}{E} = \dfrac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{4.02 \times 10^{-19}} \text{ m}$$.

Calculating, $$\lambda \approx 4.94 \times 10^{-7}\text{ m}$$.

Since $$1\text{ nm} = 10^{-9}\text{ m}$$, $$\lambda \approx 494\text{ nm}$$.

The longest (minimum-energy) wavelength capable of breaking a single $$Cl-Cl$$ bond is therefore $$\mathbf{494\ nm}$$.

Option D which is: $$494\ \text{nm}$$