How can a photon have energy when its mass is zero?

Question

How can a photon have energy when its mass is zero? According to Einstein's equation $E = mc^2$ energy depends on $mass*c^2$ Light has zero mass so the energy would be zero too but solar cells use photon's energy but how can a photon have energy when its mass is zero?

Answer 1

The E=mc^2 formula only applies to an object at rest, and light is never at rest. You want to use the more general formula:

$E^2={m_0}^2c^4+p^2c^2$

Then you can set the mass to zero.

$E=pc$

What this says is that light has momentum, which is related to its energy.

Answer 2

This is because instead of $$\dfrac{1}{2}mv^2$$ or $$E = mc^2$$ the energy of light is given by $$E = hf$$

Where h is a number called Planck's constant and f is frequency (sometimes v is used)

Here is an example, as requested:

Imagine red light with $620. nm$ wavelength. The frequency of this light is $0.483$ x $10^{15}Hz$ This makes the energy of a single photon of this light (given by $E = hf$) $2.00 eV$.