Photon Energy: Frequency and Height in a Well

[Gyroscope]

Homework Statement

A photon of frequency f falls in a well x meters of height. What is the energy of the photon when it is at the bottom of the well.

The energy of a photon is hf. It would gain mgx for falling in the well, but since his mass is zero, the energy remains the same. Isn't it?

Homework Equations

The Attempt at a Solution

 

[Dick]

If you think about conservation of energy, it would clearly have to gain the same amount of energy as a mass of size hf/c^2. Otherwise, converting energy to mass, dropping it and converting back to energy would leave you with a puzzling balance sheet.