First, we need to find the energy difference between the two energy levels n=3 and n=2 . We can do this by calculating the energy for each level and then finding the difference.E3 = -13.6 / 3^2 eV = -13.6 / 9 eV = -1.51 eVE2 = -13.6 / 2^2 eV = -13.6 / 4 eV = -3.4 eVNow, we can find the energy difference E between the two levels:E = E2 - E3 = -3.4 eV - -1.51 eV = -1.89 eVNext, we need to convert this energy difference from electron volts eV to joules J . We can do this using the conversion factor: 1 eV = 1.602 10^-19 J.E = -1.89 eV 1.602 10^-19 J/eV = -3.03 10^-19 JNow, we can use the Planck's equation to find the wavelength of light that must be absorbed for this transition:E = h c / Where E is the energy difference, h is the Planck constant 6.626 10^-34 J s , and c is the speed of light 3 10^8 m/s .Rearranging the equation to solve for : = h c / EPlugging in the values: = 6.626 10^-34 J s 3 10^8 m/s / -3.03 10^-19 J = 6.56 10^-7 mTherefore, the wavelength of light that must be absorbed for an electron in a hydrogen atom to transition from the n=3 to n=2 energy level is approximately 6.56 10^-7 m or 656 nm.