Question

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

• A. $494\text{nm}$
• B. $594\text{nm}$
• C. $640\text{nm}$
• D. $700\text{nm}$

Answer 1

The correct option is A $494\text{nm}$

we have $B.E=242\text{kJ/mol}$
$E=\frac{hc{N}_A}{\lambda }$
$\therefore \lambda =\frac{hc{N}_A}{E}$
$\Rightarrow \lambda =\frac{3\times {10}^8\times 6.626\times {10}^{-34}\times 6.02\times {10}^{23}}{(242\times {10}^3)}$
$\Rightarrow \lambda =0.494\times {10}^{-3}\times {10}^{-3}$
$\Rightarrow \lambda =0.494\times {10}^{-6}\text{m}$
$\Rightarrow \lambda =494\times {10}^{-9}\text{m}$
$\Rightarrow \lambda =494\text{nm}$
Hence option (a) is the answer.