Question
Electromagnetic radiation of wavelength $$242\,nm$$ is just sufficient to ionise the sodium atom. What is the ionisation energy of sodium per atom ?
A.
$$494.5 \times {10^{ - 6}}\,J/atom$$
B.
$$8169.5 \times {10^{ - 10}}\,J/arom$$
C.
$$5.85 \times {10^{ - 15}}\,J/atom$$
D.
$$8.214 \times {10^{ - 19}}\,J/atom$$
Answer :
$$8.214 \times {10^{ - 19}}\,J/atom$$
Solution :
$$\lambda = 242\,nm = 242 \times {10^{ - 9}}\,m$$
Energy required to ionise one atom of $$Na,E = \frac{{hc}}{\lambda }$$
$$\eqalign{
& = \frac{{\left( {6.626 \times {{10}^{ - 34}}\,J\,s} \right) \times \left( {3 \times {{10}^8}\,m\,{s^{ - 1}}} \right)}}{{242 \times {{10}^{ - 9}}m}} \cr
& = 8.214 \times {10^{ - 19}}\,J/atom \cr} $$