The energy of an electromagnetic wave is directly related to its frequency through the equation given by Planck's relation:
\[ E = h f \]
Where:
- \( E \) is the energy of a photon (the quantum of an electromagnetic wave),
- \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} , \text{J} \cdot \text{s} \),
- \( f \) is the frequency of the electromagnetic wave, measured in hertz (Hz).
This equation shows that the energy of a photon increases with an increase in frequency. Higher frequency electromagnetic waves, such as gamma rays and X-rays, carry more energy than lower frequency waves, like radio waves or microwaves.
Additionally, since the speed of light \( c \) is related to wavelength \( \lambda \) and frequency \( f \) by the equation:
\[ c = \lambda f \]
you can also express energy in terms of wavelength. By substituting \( f \) with \( \frac{c}{\lambda} \) in the energy equation, you get:
\[ E = \frac{h c}{\lambda} \]
This shows that energy is inversely proportional to wavelength, reinforcing the concept that shorter wavelengths correspond to higher energy.
In summary, the energy of an electromagnetic wave is directly proportional to its frequency and inversely proportional to its wavelength.