Question

Electromagnetic radiation of wavelength $242nm$ is just sufficient to ionize the sodium atom. Calculate the ionization energy of sodium in $kJ/mol$.

Answer 1

Electromagnetic waves

1. An electromagnetic wave is a transverse wave in nature.
2. The energy of the electromagnetic wave of wavelength $\lambda$ is defined by the form, $E=h\frac{c}{\lambda }$, where, h is the Plank constant and c is the velocity of light in free space.

Step 1: Given data

The wavelength of electromagnetic radiation is, $\lambda =242nm.$

The energy of the electromagnetic can ionize the sodium atom. So ionization energy of sodium is equal to the energy of the electromagnetic wave.

Step 2: Calculating the ionization energy of the sodium atom

Now, the energy of the electromagnetic wave is

$$\begin{gathered} E=h\frac{c}{\lambda } \\ E=\left(6.626\times {10}^{-34}\right)\times \frac{\left(3\times {10}^8\right)}{\left(242\times {10}^{-9}\right)} \\ E=8.21\times {10}^{-19} \\ E=8.21\times {10}^{-19}joule/atom. \end{gathered}$$

So, ionization energy per mole is

$$\begin{gathered} E=\left(8.21\times {10}^{-19}\right)\times \left(6.023\times {10}^{23}\right) \\ E\hspace{0.17em}=494488.3joule/mole \\ orE=494Kj/mole. \end{gathered}$$

Therefore, the ionization energy of sodium $494kj/mole.$