# Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom.

Question.

Electromagnetic radiation of wavelength $242 \mathrm{~nm}$ is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in $\mathrm{kJ} \mathrm{mol}^{-1}$.

Solution:

Energy of sodium $(E)=\frac{N_{\Lambda} h c}{\lambda}$

$=\frac{\left(6.023 \times 10^{23} \mathrm{~mol}^{-1}\right)\left(6.626 \times 10^{-34} \mathrm{Js}\right)\left(3 \times 10^{8} \mathrm{~ms}^{-1}\right)}{242 \times 10^{-9} \mathrm{~m}}$

$=4.947 \times 10^{5} \mathrm{~J} \mathrm{~mol}^{-1}$

$=494.7 \times 10^{3} \mathrm{~J} \mathrm{~mol}^{-1}$

$=494 \mathrm{~kJ} \mathrm{~mol}^{-1}$