Question

An electromagnetic radiation of wavelength 198 nm is sufficient to ionise a metal atom. Calculate the ionisation energy in $kJmo{l}^{-1},(Planckconstanth=6.6\times {10}^{-34}Js,Avogadronumber=6.02\times {10}^{23}$

Answer 1

According to Planck's quantum theory,
The energy of radiation is inversely proportional to its wavelength which is given by, $E=\frac{hc}{\lambda }$
Given,
$\lambda =198\times {10}^{-9}m$
$h=6.6\times {10}^{-34}Js$
As the electromagnetic radiation is just sufficient to ionize the sodium atom,
Ionization energy = Energy of the photon
$\therefore E=\frac{hc}{\lambda }$
$=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{198\times {10}^{-9}}$
$={10}^{-18}J$
$=10\times {10}^{-22}kJ/atom$
Thus, for the ionisation of 1 atom, energy = $10\times {10}^{-22}kJ$ is required.
$\therefore$ Energy required per mole = $10\times {10}^{-22}kJ\times 6.02\times {10}^{23}$
$=602kJmo{l}^{-1}$