# On the EM Spectrum, which type of wave has the most energy?

Apr 7, 2018

Gamma rays.

#### Explanation:

A general guideline tends to be : short wavelength, high energy . But here is a way to show which waves are the most energetic:

The energy of a wave is given by the equation:

$E = h f$

$h$=Planck's constant (6,6261·10^(-34) Js^-1)
$f$=frequency of the wave

Hence we can see that the energy of a wave is proportional to its frequency, as the other term is a constant.

Then we can ask ourselves, which waves are the ones with the highest frequency?

If we use another equation:

$c = f \lambda$

$c$=speed of light ,$3.0 \times {10}^{8} m {s}^{-} 1$
$f$=frequency (Hz)
$\lambda$=wavelength in meters.

Then we can see that, as $c$ is constant in a vacuum, and $f$ is high, then $\lambda$, the wavelength, must be low.
Now if we use this diagram of the EM-spectrum which show wavelengths:

We can thus conclude that the waves that have the shortest wavelength are gamma rays, and thus they are the most energetic because they must also have the highest frequency.