Final answer:
The maximum wavelength emitted when an electron recombines with a hole in zinc oxide, with a band gap of 3.2 eV, is found to be approximately 389 nanometers using Planck's equation relating energy and wavelength.
Step-by-step explanation:
The band gap between the valence and conduction bands in zinc oxide (ZnO) is 3.2 eV. This energy gap is critical in determining the wavelength of the electromagnetic radiation emitted when an electron falls from the conduction band to the valence band and recombines with a hole. To find the maximum wavelength of the emitted radiation, we can use the energy-wavelength relationship from Planck's equation, which is E = hc/λ, where 'E' is the energy in electron volts (eV), 'h' is Planck's constant (4.135667696 × 10-15 eV·s), 'c' is the speed of light (2.998 × 108 m/s), and 'λ' is the wavelength in meters.
By rearranging Planck's equation to solve for the wavelength, we get λ = hc/E. Substituting the values in, we find λ = (4.135667696 × 10-15 eV·s × 2.998 × 108 m/s) / 3.2 eV, which gives us a maximum wavelength of approximately 389 nanometers (nm). Therefore, the maximum wavelength that can be emitted in this process is 389 nm.