Photon Theory Of Light - Practice Questions & MCQ

Photon theory of light -

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. The energy of one quantum is given by, hν , where h is the Planck's constant and ν is the frequency.

$
E=h \nu=\frac{h c}{\lambda}
$

where $\mathrm{c}=$ Speed of light, $\mathrm{h}=$ Plank's constant $=6.6 \times 10^{-34} \mathrm{~J}-\mathrm{sec}$
$\nu=$ Frequency in $\mathrm{Hz}, \lambda=$ Wavelength of light.

$
E(\mathrm{eV})=\frac{12400}{\lambda}
$

(In the form of eV)
Properties of Photon
1. Photon is a packet of energy (or) particles of light and travels with speed of light in a straight line.
2. Energy of photon is given as $E=h \nu$ and it depends on frequency and it does not change with change in medium.
3. Photons are electrically neutral and not effected by electric and maginetic field.
4. Photons does not exist at rest i.e., it is a moving particle

$
p=\frac{h}{\lambda}
$

5. Momentum of photon is given as
6. All photons of light of a given frequency or wavelength have same energy or momentum irrespective of light intensity
7. Photons can interact with other particles like electrons, which can be seen in Compton effect
8. Photons can be created or destroyed when the radiation is emitted or absorbed i.e no of photons is not conserved during collision
9. The dynamic mass of the photon is $m=E / c^2$, where $E$ is the energy of the photon
10. During photon-electron collision, the momentum and total energy are conserved
11. Photons do not decay on their own
12. The energy possessed by the photon can be transferred to other particles when it interacts with other particles

After energy now let us discuss the mass of the photon.

Mass of photon : 

You will study in the theory of relativity that the rest mass of any body is given by - 

$
m_v=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}
$

Where: $m_v=$ Relativistic mass ( kg )
$m_o=$ Rest mass (kg)
$v=$ velocity $\left(\mathrm{ms}^{-1}\right)$
$c=$ speed of light $=3 \times 10^8 \mathrm{~ms}^{-1}$
As the velocity of photon is same as speed of light, so from the above equation we can write that - $m_o=0$. 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}
$

It is also called as kinetic mass of the photon.
Momentum of the photon -
As the momentum of any body is $=m \cdot v$
Here the velocity = c, i.e., speed of light. So, we can write that -

$
p=m \times c=\frac{E}{c}=\frac{h \nu}{c}=\frac{h}{\lambda}
$
 

Note -

1. In a photon particle collision, total energy and total momentum will be conserved but the number of photons may be changed. 

2. All photons of light of a particular freq. (or) wavelengths have the same energy and momentum whatever may be the intensity.