In a collision between a photon and a free electron, which is correct, if all the photon energy were transferred to the electron.a)Energy is not conserved.b)momentum is not conserved.c)Both is not conserved.d)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Conservation of momentum in a photon-electron collision

In a collision between a photon and a free electron, it is important to consider the conservation of momentum. Momentum is a fundamental concept in physics that describes the motion of an object. According to Newton's laws of motion, the total momentum of a closed system remains constant unless acted upon by an external force.

Photon and electron momentum

A photon is a massless particle that travels at the speed of light in a vacuum. It has both energy and momentum, which are related by the equation E = pc, where E is the energy, p is the momentum, and c is the speed of light.

An electron, on the other hand, has both mass and momentum. Its momentum is given by the equation p = mv, where p is the momentum, m is the mass, and v is the velocity.

Collision scenario

In the collision between the photon and the free electron, let's assume that all the energy of the photon is transferred to the electron. This means that the photon loses all its energy, and the electron gains the same amount of energy.

Conservation of momentum in the collision

According to the principle of conservation of momentum, the total momentum before and after the collision should be the same. If the momentum is not conserved, it would imply the presence of an external force, which is not the case in this scenario.

Before the collision, the photon has momentum given by p_photon = E_photon/c, where E_photon is the energy of the photon. The free electron, being at rest, has zero momentum.

After the collision, the electron gains the energy of the photon, so its momentum becomes p_electron = E_photon/c.

Conclusion

Since the momentum of the electron changes from zero to a non-zero value, it is clear that momentum is conserved in the collision between the photon and the free electron. Therefore, the correct answer is option 'B' - momentum is conserved.

Answer

Let E₁ = hv energy of photon

momentum of photon

energy of electron
P₂ = momentum of electron
If all energy is to be transferred to the electron hv

Electron momentum

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