Ionisation Energy of Sodium

To calculate the ionisation energy of sodium, we need to first understand the concept of ionisation and the relevant equation involved.

Ionisation Process
The ionisation process involves the removal of an electron from an atom or molecule, resulting in the formation of a positively charged ion. In the case of sodium, ionisation can be represented as follows:
Na + Energy → Na+ + e-

Equation for Ionisation Energy
The ionisation energy (IE) is defined as the minimum amount of energy required to remove an electron from an atom or ion in its gaseous state. Mathematically, it can be expressed as:
IE = -ΔE/n

where ΔE is the change in energy and n is the number of moles of atoms or ions.

Calculating Ionisation Energy
Given that the electromagnetic radiation has a wavelength of 242 nm, we can calculate the energy of a single photon using the equation:
E = hc/λ

where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength.

Converting the wavelength to meters:
λ = 242 nm = 242 x 10^-9 m

Plugging the values into the equation:
E = (6.626 x 10^-34 J·s)(2.998 x 10^8 m/s) / (242 x 10^-9 m)
E ≈ 8.207 x 10^-19 J

To convert the energy to kilojoules per mole, we need to divide by Avogadro's number (6.022 x 10^23), and then multiply by the molar mass of sodium (22.99 g/mol):
IE = (8.207 x 10^-19 J) / (6.022 x 10^23) * (22.99 g/mol) * (1 kJ/1000 J)
IE ≈ 148.9 kJ/mol

Therefore, the ionisation energy of sodium is approximately 148.9 kJ/mol.

Summary
The ionisation energy of sodium can be calculated by determining the energy of a photon with a given wavelength. By using the equation E = hc/λ and converting the energy to kilojoules per mole, we can find that the ionisation energy of sodium is approximately 148.9 kJ/mol.