Final answer:
To calculate the ionization energy of sodium, one uses the equation E = hc/λ, where E is the energy of a photon, h is the Planck constant, c is the speed of light, and λ is the wavelength of light that can ionize sodium. The energy obtained is then converted from joules to kilojoules per mole using Avogadro's number.
Step-by-step explanation:
The student is asking about the ionization energy of a sodium atom which can be calculated using the wavelength of electromagnetic radiation capable of ionizing it. The wavelength of radiation given is 242 nm. To find the ionization energy, we use the equation that relates the energy of a photon to its wavelength: E = hc/λ. Here, h is the Planck constant (6.626 x 10^{-34} J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light in meters.
First, convert the wavelength from nanometers to meters by multiplying with 1 x 10^{-9} m/nm. Then, plug the values into the equation to find the energy in joules. Finally, convert the energy to kilojoules per mole (kJ/mol) by multiplying the energy per photon by Avogadro's number (6.022 x 10^{23} mol^{-1}) and dividing by 1000.
The ionization energy corresponds to the minimum energy required to remove the most loosely bound electron from a neutral atom in its ground state, which in this case is provided by the photon with a wavelength of 242 nm.