Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. This means that the energy of the photon is equal to the ionisation energy of sodium. Ionisation energy is the minimum amount of energy required to remove an electron from an atom or ion in its ground state.


The formula for the ionisation energy is:
IE = hν = (13.6 eV) * (Z^2/n^2)

Where,
h = Planck's constant = 6.626 × 10^-34 J s
ν = frequency of the radiation in Hz
Z = atomic number of the element
n = principal quantum number of the electron


The frequency of the radiation can be calculated using the formula:
c = λν
Where,
c = speed of light = 3 × 10^8 m/s
λ = wavelength of the radiation = 242 nm = 242 × 10^-9 m

ν = c/λ = (3 × 10^8 m/s) / (242 × 10^-9 m) = 1.24 × 10^15 Hz

The atomic number of sodium is 11 and the electron that is removed is in the n=2 shell.

IE = hν = (6.626 × 10^-34 J s) * (1.24 × 10^15 Hz) = 8.21 × 10^-19 J

Converting to KJ/mol:
1 J/mol = 0.001 KJ/mol
1 eV = 96.48 KJ/mol

IE = (8.21 × 10^-19 J) * (1 eV/1.602 × 10^-19 J) * (1/96.48 KJ/mol) = 5.14 KJ/mol


The ionisation energy of sodium is calculated to be 5.14 KJ/mol. This means that it takes 5.14 KJ of energy to remove one mole of electrons from one mole of sodium atoms in their ground state.