III. The energy of a photon is directly proportional to wavelength but inversely proportional to wave number.

The statement provided is partially incorrect. The energy of a photon is inversely proportional to its wavelength and directly proportional to its wave number.

Here's the step-by-step explanation:

1. The energy (E) of a photon can be calculated using the equation E = hv, where h is Planck's constant and v is the frequency of the light.

2. The frequency (v) can be related to the wavelength (λ) by the equation v = c/λ, where c is the speed of light. Substituting this into the first equation gives E = hc/λ. This shows that the energy of a photon is inversely proportional to its wavelength.

3. The wave number (ν) is defined as the reciprocal of the wavelength, ν = 1/λ. Substituting this into the equation for energy gives E = hcν. This shows that the energy of a photon is directly proportional to its wave number.