What Are the Momentum and Energy of Photons from a Decaying Particle?

In summary, the conversation is about a particle with rest mass m that decays into 2 photons and the task is to find expressions for the momentum of the particle and the energy of each photon, both in terms of m. The suggested steps are to start with the kinetic energy being twice the rest energy, solve for the energy and momentum, and then use the Lorentz transformation to find the energy of each photon in the frame moving with the particle's velocity.
  • #1
da_warped_1
7
0
hi wondering if i could get a little help with this question

A particle with rest mass m has kinetic energy equal to twice its rest energy. The particle decays into 2 photons which emerge in opposite directions, one traveling in the same direction as the particle before its decay. Find expressions, in terms of m for:

(a) the momentum of the particle
(b) the energy of each of the 2 photons

thanks for any help.
 
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  • #2
What help do you want? Where is the difficulty? In other words, what have you done on this yourself?
 
  • #3
da_warped_1 said:
hi wondering if i could get a little help with this question

A particle with rest mass m has kinetic energy equal to twice its rest energy. The particle decays into 2 photons which emerge in opposite directions, one traveling in the same direction as the particle before its decay. Find expressions, in terms of m for:

(a) the momentum of the particle
(b) the energy of each of the 2 photons

thanks for any help.
For (a), start with T=E-m=2m. Solve for E and then for p.
For (b), LT each photon's energy in the particle's rest frame (k=m/2),
to the frame moving with velocity v=p/E.
 

Related to What Are the Momentum and Energy of Photons from a Decaying Particle?

1. What are particles in the context of special relativity?

Particles refer to any physical entity that has mass and occupies space. In the context of special relativity, particles are considered to be fundamental building blocks of matter and are described by their energy, momentum, and mass. They can also be classified as either bosons or fermions based on their spin characteristics.

2. How does special relativity affect the behavior of particles?

Special relativity states that the laws of physics are the same for all observers moving at constant velocities. This means that particles will behave the same way regardless of the observer's frame of reference. Additionally, special relativity predicts that particles with mass can never reach the speed of light, and their mass will increase as they approach the speed of light.

3. What is the relationship between energy and mass in special relativity?

In special relativity, energy and mass are closely related through the famous equation E=mc², where E is energy, m is mass, and c is the speed of light. This equation shows that mass and energy are interchangeable and can be converted into one another. This is also why particles with mass cannot reach the speed of light, as it would require infinite energy.

4. Can particles travel faster than the speed of light in special relativity?

No, according to special relativity, particles with mass can never reach the speed of light. This is because as an object approaches the speed of light, its mass increases, and it would require an infinite amount of energy to accelerate it to the speed of light. Particles with zero mass, such as photons, can travel at the speed of light, but not faster.

5. How does special relativity impact our understanding of particle interactions?

Special relativity has greatly influenced our understanding of particle interactions. It explains the relationship between energy and mass, allowing us to understand the behavior of particles at high speeds. It also plays a crucial role in particle accelerators, where particles are accelerated to near-light speeds in order to study their interactions and properties.

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