Question

Calculate the wavelength of the radiation which would cause the photo-dissociation of chlorine molecule if the Cl-Cl bond energy is 243 kJ/mol.

• A. $493nm$
• B. $4900\mu m$
• C. $4900nm$
• D. $493m$

Answer 1

The correct option is A $493nm$

Let the wavelength of the radiation be $\lambda$.
Energy required to break one Cl-Cl bond = $\frac{\text{Bond energy per mole}}{\text{Avogadro's number}}$
Energy required = $\frac{243\times {10}^3}{6.023\times {10}^{23}}$ J = $4.034\times {10}^{-19}$ J
From Planck's quantum theory,
E = $\frac{hc}{\lambda }$ or $\lambda =\frac{hc}{E}$
$\lambda =\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{4.034\times {10}^{-19}}=4.93\times {10}^{-7}$
$\lambda =4.93\times {10}^{-7}$ m = 493 nm