JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Photon

According to Eienstein's quantum theory light propagates in the bundles (packets or quanta) of energy, each bundle being called a photon and possessing energy.

(1) Energy of photon : Energy of photon is given by

\[E=h\nu =\frac{hc}{\lambda };\]  where c = Speed of light, h = Plank's constant \[=6.6\times {{10}^{-34}}\,J-\sec ,\]  n  = Frequency in Hz, \[\lambda =\]Wavelength of light. 

In electron volt \[E(eV)=\frac{hc}{e\lambda }=\frac{12375}{\lambda \,({\AA})}\] \[\approx \frac{12400}{\lambda \,({\AA})}\]

(2) Mass of photon : Actually rest mass of the photon is zero. But it's effective mass is given as

\[E=m{{c}^{2}}=h\nu \]\[\Rightarrow \]\[m=\frac{E}{{{c}^{2}}}=\frac{h\nu }{{{c}^{2}}}=\frac{h}{c\lambda }\].

This mass is also known as kinetic mass of the photon

(3) Momentum of the photon

Momentum \[p=m\times c=\frac{E}{c}=\frac{h\nu }{c}=\frac{h}{\lambda }\]

(4) Number of emitted photons : The number of photons emitted per second from a source of monochromatic radiation of wavelength \[\lambda \] and power P is given as \[(n)=\frac{P}{E}=\frac{P}{h\nu }=\frac{P\lambda }{hc}\]; where E = energy of each photon

(5) Intensity of light (I) : Energy crossing per unit area normally per second is called intensity or energy flux

i.e.  \[I=\frac{E}{At}=\frac{P}{A}\]             \[\left( \frac{E}{t}=P=\text{radiation}\,\text{power} \right)\]

At a distance r from a point source of power P intensity is given by \[I=\frac{P}{4\pi {{r}^{2}}}\]\[\Rightarrow \]\[I\propto \frac{1}{{{r}^{2}}}\]

(6) Number of photons falling per second (n) : If P is the power of radiation and E is the energy of a photon then \[n=\frac{P}{E}\]