Question

Calculate the wavelength of the radiation which would cause the photodissociation of chlorine molecule if the $Cl-Cl$ bond energy is $243$ $kJ$ ${mol}^{-1}$.

Answer 1

$Explanation:$

According to Planck's law,

$E=hc/\lambda \to \left(1\right)$

where,

$E=$Band energy$=243KJ/mol$

$(\because 1KJ/mol=0.0167\times {10}^{-19})$

$E=0.0167\times 243\times {10}^{-19}=4.067\times {10}^{-19}$

$h=$Planck's constant$=6.625\times {10}^{-3}$

$c=$Speed of light$=3\times {10}^{8}m/s$

$\lambda =$Wavelength $=?$

From equation 1 we get,

$\lambda =hc/E$

$\lambda =\left(\right(6.625\times {10}^{-3})\times (3\times {10}^{8}m/s\left)\right)/(4.067\times {10}^{-19})=4.887\times {10}^{-7}m$

$\because 1nm=10-9$

$\therefore \lambda =488nm$

$Hencethecorrectansweris\therefore \lambda =488nm$