Question

Say for example a questions says that electromagnetic radiation of walevength 100 nm is just sufficient to ionize a sodium atom.
So what exactly does this statement refer to.
What does it mean??

Answer 1

Dear Student

This simply means that to ionise the Na atom or one atom of Na, we require a wavelength, $\lambda$ = 100 nm or 100 x 10^-9 m
Thus, the Energy of Photon, E = $\frac{hc}{\lambda }$
where, h = Planck's Constant, 6.626 x 10^-34 Js ; c = Speed of Light, 3 x 10⁸ m/s

E = $\frac{6.626x{10}^{-34}x3x{10}^8}{100x{10}^{-9}}$ = 0.19878 x 10^-17 J atom^-1
So, the ionisation energy for 1 mole of sodium atom = $\frac{0.19878x{10}^{-17}x6.02x{10}^{23}}{1000}$ = 1.1966 x 10³ KJ mol^-1

Regards