# How can a photon have energy when its mass is zero? [duplicate]

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?

• possible duplicate of Does $E = mc^2$ apply to photons? Commented Apr 9, 2015 at 4:36
• us youngin's have to stick together Commented Apr 9, 2015 at 5:08

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.

• actually, if you use the deprecated concept of "rest mass" (now usually called "invariant mass") and "relativistic mass", then $E=mc^2$ works in any case. for bodies with rest mass, the relativistic mass is $$m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$$ and swinging that around is $$m_0 = m \sqrt{1-\frac{v^2}{c^2}}$$ now if $m = \frac{E}{c^2} = \frac{h \nu}{c^2}$ is finite and $v=c$, then you can see that the rest mass $m_0 = 0$. Commented Apr 10, 2015 at 2:02
• @robert bristow-johnson I agree, but like you said, it's a deprecated concept, and thus not mentioned in my answer. You'll notice I write the formula using $m_0$ rather than $m$, as is fairly standard to avoid confusion. Commented Apr 10, 2015 at 21:19

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 $E = hf$) $2.00 eV$.

• Commented Apr 10, 2015 at 5:46