Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol–1.

To find the ionization energy of sodium using the given wavelength of electromagnetic radiation, we can start by applying the relationship between energy, wavelength, and constants from physics. The ionization energy is essentially the energy required to remove an electron from an atom, and we can calculate it using the formula derived from Planck's equation.

Understanding the Relationship

The energy (E) of a photon can be calculated using the equation:

E = (hc) / λ

Where:

• h is Planck's constant (6.626 x 10^-34 J·s)
• c is the speed of light in a vacuum (3.00 x 10⁸ m/s)
• λ is the wavelength in meters

Converting Wavelength

The given wavelength is 242 nm. First, we convert this to meters:

242 nm = 242 x 10^-9 m

Plugging in the Values

Now we can substitute the values into the equation:

E = (6.626 x 10^-34 J·s * 3.00 x 10⁸ m/s) / (242 x 10^-9 m)

Calculating the Energy

Calculating the numerator:

6.626 x 10^-34 * 3.00 x 10⁸ = 1.9878 x 10^-25 J·m

Now dividing by the wavelength:

E = (1.9878 x 10^-25 J·m) / (242 x 10^-9 m) = 8.226 x 10^-19 J

Converting to kJ/mol

The energy we calculated is in joules per photon. To find the ionization energy in kJ/mol, we convert joules to kilojoules and then multiply by Avogadro's number (6.022 x 10²³ mol^-1):

Ionization energy in kJ/mol = (8.226 x 10^-19 J) * (1 kJ / 1000 J) * (6.022 x 10²³ mol^-1)

Ionization energy = 8.226 x 10^-19 * 6.022 x 10²³ / 1000

Ionization energy = 496.6 kJ/mol

Final Result

Therefore, the ionization energy of sodium is approximately 497 kJ/mol. This value represents the energy required to remove one mole of electrons from sodium atoms, indicating the strength of the bond between the electrons and the nucleus in the sodium atom.