Wave shows particle properties when the energy of photon is discrete.
Electromagnetic waves irradiated on certain surfaces experience change in momentum when the photons collide with electrons in the atomic structure.
Energy of a photon,
\[
E=h f=\frac{h c}{\lambda}
\]
where \(h=\) Planck’s constant \(\int=\) frequency of light wave
\(\lambda=\) wavelength
\(c=\) wave speed
Power, \(P\) of an electromagnetic wave depends on the number of photons emitted per unit time.
\[
P=n h f=\frac{n h c}{\lambda}
\]
where \(n=\) number of photons emitted per second
Example
A neon bulb of \(65 W\) radiates light with a wavelength of \(648 nm\). How many photons are emitted in one second?\[
\begin{aligned}
P & =\frac{n h c}{\lambda} \\
n & =\frac{P \lambda}{h c} \\
& =\frac{(65)\left(648 \times 10^{-9}\right)}{\left(6.63 \times 10^{-34}\right)\left(3 \times 10^8\right)} \\
& =2.12 \times 10^{20} s ^{-1}
\end{aligned}
\]
Example
A beacon emits red light of frequency \(400 THz\). If \(3.5 \times 10^{16}\) photons are emitted at millisecond intervals, determine the power of the light source.
\[
\begin{aligned}
P & =n h f \\
& =\left(\frac{3.5 \times 10^{16}}{1 \times 10^{-3}}\right)\left(6.63 \times 10^{-34}\right) \\
& \left(400 \times 10^{12}\right) \\
& =9.28 W
\end{aligned}
\]