Distinction between Spontaneous and Stimulated Emission of Radiation

Some of the differences between spontaneous and stimulated emission of radiation are given as follows:

1. In spontaneous emission, an atom in excited state falls to the ground state on its own without any incident photon while in stimulated emission transition takes place by stimulating photons or by an external agency.

2. In stimulated emission for each incident photon there are two outgoing photons in the same direction while in spontaneous emission the emitted photons move randomly in any direction.

3. The photons emitted in spontaneous emiss ion have a random phase and hence are incoherent while in stimulated emission the emitted photons are in phase and hence are coherent.

4. The rate of spontaneous emission is proportional to only the number of atoms in the excited state while the rate of stimulated emission is proportional to the number of atoms left in the excited state as well as on the energy density of the incident radiation.

5. In stimulated emission of radiation an amplified beam is achieved while in spontaneous emission there is no such amplification.

6. The light emitted through the spontaneous emission is not monochromatic while in stimulated transition monochromatic radiation is obtained.

7. Spontaneous emission is not controllable from outside while stimulated emission is controllable from outside.

8. In spontaneous emission, the net intensity is proportional to the number of radiating atoms while in stimulated emission it is proportional to the square of the number of radiation atoms.

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Nuclear Fuel Cycle

The nuclear fuel cycle refers to the series of steps involved in the production of nuclear power, from the mining of uranium ore to the disposal of nuclear waste.

Uranium Mining: The first step in the nuclear fuel cycle is the mining of uranium ore, which is typically extracted from underground mines or open-pit mines.

Uranium Enrichment: After the uranium ore is mined, it is transported to a facility where it is enriched, which involves increasing the proportion of uranium-235 isotopes in the uranium. This is done using centrifuges or other methods.

Fuel Fabrication: The enriched uranium is then processed into fuel pellets, which are loaded into fuel rods that will be used in nuclear reactors.

Nuclear Reactors: The fuel rods are then placed in a nuclear reactor, where they undergo a nuclear fission chain reaction that produces heat, which is used to generate electricity.

Spent Fuel Storage: After the fuel rods have been used in the reactor for several years, they become depleted and are considered "spent." They are removed from the reactor and stored in cooling pools at the nuclear power plant.

Reprocessing: In some countries, the spent fuel is then sent to a reprocessing facility, where the remaining uranium and plutonium in the fuel rods can be extracted and reused to make new fuel.

Disposal: Eventually, the spent fuel will need to be disposed of. In some countries, it is stored in long-term storage facilities, while in others, it is reprocessed or disposed of in deep geological repositories.

The nuclear fuel cycle is a complex process that requires careful management to ensure safety and minimize the risk of nuclear accidents or proliferation. Proper management and disposal of nuclear waste is a critical aspect of the nuclear fuel cycle, as it can remain radioactive for thousands of years and pose a hazard to human health and the environment.

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Absorption of all the energy of a incident photon by a free electron

A free electron cannot absorb all the energy of a Photon in mutual interaction.

Let us consider that a photon of energy $h \nu$ and momentum $\frac{h\nu}{c}$ collides with the free electron of mass $m$ at rest and the photon transfers its total energy and momentum to the electron. If $v$ is the velocity of the electron after a collision, its energy will be $ \frac{1}{2}mv^{2}$ and momentum $mv$.

If total incident energy $E$ absorb by an electron then applying the laws of conservation of energy and momentum, we have

Total energy before the collision= Total energy after the collision

$h \nu = \frac{1}{2}mv^{2} \qquad(1)$

According to de Broglie Hypothesis, the momentum of a particle

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

$P=\frac{h \nu}{c} \qquad \left(\because \lambda=\frac{c}{\nu} \right)$

$mv=\frac{h \nu}{c} \qquad \left(\because P = mv \right)$

$h \nu = mvc \qquad(2)$

From equation $(1)$ and equation $(2)$

$\frac{1}{2}mv^{2}= m v c$

$\frac{1}{2}mv^{2}=m v c$

$v=2c$

Thus, the velocity of an electron comes out to be $2c$ which is not possible according to relativistic mechanics. Hence, a free electron cannot absorb all the energy of an incident photon.

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