Why does wavelength determine the energy of a photon? The professor for my first-year university chemistry class remarked that the wavelength of a photon determines its energy. Why is it that the case?
I've only completed high-school physics so far, so please bear that in mind in answering this question. 
Thank you. 
 A: Well, actually it doesn't. Knowing the wavelength allows you to calculate the energy, but it does not "determine" it in a causal way.
Energy (E), wavelength ($\lambda$) and frequency ($\nu$) are related by $$E = h\nu =\frac{hc}{\lambda}$$ so if you know the wavelength or the frequency you can determine the energy. I think his use of "determine" confused you.
A: Why does the wavelength determine a photon's energy?
In the 19th century, it was thought that the energy of light was determined only by its intensity.  Then, experiments, particularly the photoelectric effect, showed that this was not so: a low-intensity short-wavelength light can cause reactions that intense light of a longer wavelength cannot.  Thus, from experiment, shorter wavelength must mean higher energy.
Next, there was the problem of black body radiation.  In thermal equilibrium, bodies glow but the classical theory predicted the wrong spectrum.   In 1905, Einstein created a theory that predicted the correct black body spectrum on the assumption that light is made of particles whose energy is inversely proportional to wavelength.
So, in other words, to get theory and experiment to match, we have to assume that the energy of a photon is inversely proportional to its wavelength.
