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

To calculate the ionization energy of sodium when electromagnetic radiation of wavelength 242 nm is used, we apply the formula:

E = hc / λ

Step 1: Substitute the known values:

• h = 6.626 × 10-34 J·s
• c = 3.0 × 108 m/s
• λ = 242 nm = 242 × 10-9 m

Calculation:

E = (6.626 × 10^-34 × 3.0 × 10⁸) / (242 × 10^-9)

E = 8.214 × 10^-19 J (energy per photon)

Step 2: Convert this energy to kJ/mol. Multiply the energy of one photon by Avogadro's number (6.022 × 1023 mol-1) and convert joules to kilojoules (1 kJ = 1000 J):

E_mol = 8.214 × 10^-19 × 6.022 × 10²³

E_mol = 494.4 kJ/mol

Thus, the ionization energy of sodium is 494 kJ/mol when electromagnetic radiation of wavelength 242 nm is used.

Key Points

• The electromagnetic radiation of wavelength 242 nm provides enough energy to remove one electron from a sodium atom.
• The formula E = hc / λ helps calculate the energy of the radiation.
• The calculated energy is converted from joules per photon to kilojoules per mole using Avogadro’s number.