Question

Calculate the wavelength of the radiation which would cause the photodissociation of a chlorine molecule if the $Cl-Cl$ bond energy is $240{\text{kJ mol}}^{-1}$.
Take $h=6.6\times {10}^{-34}\text{J s},N_A=6\times {10}^{23}$

• A. $495\text{nm}$
• B. $400\text{nm}$
• C. $500\text{nm}$
• D. $600\text{nm}$

Answer 1

The correct option is A $495\text{nm}$

$\text{Energy required to break one}Cl-Cl\text{bond}\left(E\right)=\frac{\text{Bond energy per mole}}{\text{Avogadro number}}$

$\Rightarrow E=\frac{240\times 1000}{6\times {10}^{23}}\text{J}$

Let the wavelength of the photon that breaks one $Cl-Cl$ bond be $\lambda$.
We know that:
$\lambda =\frac{hc}{E}$
$\lambda =\frac{6.6\times {10}^{-34}\times 3\times {10}^8\times 6\times {10}^{23}}{240\times 1000}$

$\lambda =4.95\times {10}^{-7}\text{m}=495\text{nm}$