Question

Calculate the wavelength of the radiation that would cause photo dissociation of oxygen molecule if the $O=O$ bond energy is $498\text{kJ/mol}$ .
(take Avogadro's number to be $6\times {10}^{23}$, and Planck's constant (h) = $6.6\times {10}^{-34}\text{J s}$)

• A. $8.72\times {10}^{-7}\text{m}$
• B. $9.25\times {10}^{-10}\text{m}$
• C. $2.38\times {10}^{-7}\text{m}$
• D. $4.95\times {10}^{-7}\text{m}$

Answer 1

The correct option is C $2.38\times {10}^{-7}\text{m}$

Bond Energy of one mole of $O_2=498\text{kJ}$
Bond energy per molecule of $O_2$ $=\frac{\text{energy for one mole in joules}}{\text{Avogadro's number}}$
$\text{Energy per molecule}=\frac{498000}{6\times {10}^{23}}$
$=83\times {10}^{-20}$
Wavelength of radiation
$E=\frac{hc}{\lambda }$
$83\times {10}^{-20}=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{\lambda }$
$\lambda =2.38\times {10}^{-7}\text{m}$