We have seen that the electromagnetic wave cannot have an arbitrarily small strength: it must have a minimum energy \( E \) which corresponds to one photon. But what is the value of \( E \)?
This question as answered by Max Planck. He gave the answer in terms of the frequency of the electromagnetic wave.
What is the frequency of a wave? Imagine standing at one place as the wave moves past you. The frequency is the number of up and down oscillations you see each second. The frequency is usually denoted by the symbol \( \nu.\)
Planck found that the energy of a photon is proportional to the frequency; more precisely
where \( h \) is the Planck constant.
The frequency \( \nu \) of an electromagnetic wave is related to the wavelength \( \lambda \) in a simple way
where \( c \) is the speed of light
\[\require{color}\colorbox{yellow} {$c ~=~ 3 \times 10^{8} \,\, m/s $}\]Thus the energy of the photon can be written as
We see that photons with long wavelength have low energy and photons with short wavelength have high energy.
While the above relation gives the energy of a photon for any wavelength \( \lambda \), we would like to get some feeling for what such energies can do.
 
 
 
In 1900, Max Planck presented the conjecture that electromagnetic wave energy came in discrete units, given by the relation \( E=h \nu \).