Question

An electromagnetic radiation of wavelength 242 nm is just sufficient to ionize a sodium atom. The ionization energy of sodium in $kJmo{l}^{-1}$ is .

• A. 394.5
• B. 494.5
• C. 594.5

Answer 1

The correct option is B 494.5

We know that c = $\nu \lambda$ $\Rightarrow$ $\nu$ = $\frac{c}{\lambda }$

By Planck's theory,

E = $h\nu$ $\Rightarrow$ E = $\frac{hc}{\lambda }$

Now , the energy associated with a photon of 242 nm is:

$\frac{hc}{\lambda }$ = $\frac{6.626\times {10}^{-34}\times 3.0\times {10}^8}{242\times {10}^{-9}}$

= 8.21 $\times$ ${10}^{-19}$ J

Since one atom of Na requires = 8.21 $\times$ ${10}^{-19}$J for ionization,

6.023 $\times$ ${10}^{23}$ atoms of Na would require an ionization energy of:

8.21 $\times$ ${10}^{-19}$ $\times$ 6.023 $\times$ ${10}^{23}$ = 49.45 $\times$ ${10}^4$

= 494.5 kJ ${mol}^{-1}$