Question

An electromagnetic radiation of wavelength $242nm$ is just sufficient to ionise a sodium atom. Calculate the ionisation energy of sodium in kJ/mol?

• A. $494.5$
• B. $594.5$
• C. $694.5$
• D. $794.5$

Answer 1

Answer: (A)

$494.5$

From $E=hv$ or $hc/\lambda$

We have

$\lambda =242$nm

$=242\times {10}^{-9}$m

$c=3\times {10}^8$m/s

$h=6.62\times {10}^{-34}$ Js

Now putting these values in the equation, we get

$E_1=\frac{(6.62\times {10}^{-34}Js\times 3\times {10}^{8}m/s)}{(242\times {10}^{-9}m)}$

$=0.0821\times {10}^{-17}$J/atom

$E_n=E_1\times N_A\times \frac{1}{1000}=\frac{(0.082\times {10}^{-17})\times 6.022\times {10}^{23}}{\left(1000\right)}$

$=494.1$ kJ/mol

Hence, option $A$ is correct .