The ionization energy of sodium in kJ mol⁻¹, if electromagnetic radiation of wavelength 242 nm is just sufficient to ionize sodium atom is _______.

Solution

Chemistry ma’am · 3 steps

Just sufficient means one photon carries exactly the energy to remove one electron, so find hc/λ.

1. One photon, one atom. Radiation that is just sufficient to ionize means each photon gives one sodium atom exactly its ionization energy. So the energy of one photon equals the ionization energy of one atom.

   E = hc/λ = (6.626 × 10⁻³⁴)(2.998 × 10⁸)/(242 × 10⁻⁹) = 8.21 × 10⁻¹⁹ J

2. Scale to a mole. Multiply by Avogadro's number: 8.21 × 10⁻¹⁹ × 6.022 × 10²³ = 4.943 × 10⁵ J mol⁻¹. Divide by 1000 to get 494.3 kJ mol⁻¹.
3. So. The ionization energy of sodium is about 494 kJ mol⁻¹.

The idea to keep. Ionization energy from a wavelength: E = hc/λ gives energy per atom. Convert nm to m first, then multiply by N_A and divide by 1000 for kJ per mole.

Answer from the NTA final answer key. Solution by PrepWiser.