Calculation of momentum of relativistic particles

In summary, a particle of mass M decays at rest into a massless particle and another particle of mass m. The momentum of the massless particle is zero, and the momentum of the particle with mass m can be calculated using the equation E2 = m2c4 + p2c2. However, the exact solution may not be found in introductory textbooks and further research may be needed.
  • #1
physicsblr
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Homework Statement


A particle of mass M decays at rest into a massless particle and another particle of mass m. The magnitude of the momentum of each of these relativistic particles is:


Homework Equations



E = γmc2; p=γmv

The Attempt at a Solution


Pf-Pi = 0; but the particle is at rest, so pi = 0; and the momentum of massless particle = 0;
unable to start up with exact condition. Tried equating initial and final energies also, but not getting the right answer. Please help.
 
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  • #2
physicsblr said:
and the momentum of massless particle = 0

This isn't correct. Look in your notes and/or text for the relationship between energy and momentum for a massless particle.
 
  • #3
No, I tried the relation E2 = m2c4+p2c2 also, am not getting right answer. There are no explanations of this in my text graduation textbooks. These are pg level questions.

I did substitute E2 = M2c4 (initial energy) and onto r.h.s, p2c2+m2c4+p2c2 - p2c2 is the kinetic energy of the massless particle and m2c4+p2c2 for the particle of mass m.

Please give a solution if possible, am taking so much time to google n check. I am already running out of time for my entrance exam next week.
 

1. What is the formula for calculating the momentum of a relativistic particle?

The formula for calculating the momentum of a relativistic particle is p = mv/√(1 - v^2/c^2), where p is the momentum, m is the mass of the particle, v is its velocity, and c is the speed of light in a vacuum.

2. How is the momentum of a relativistic particle different from a non-relativistic particle?

The momentum of a relativistic particle takes into account the effects of special relativity, which means that as the particle approaches the speed of light, its mass increases and its momentum increases accordingly. This is in contrast to a non-relativistic particle, where the momentum is simply p = mv.

3. Can the momentum of a relativistic particle ever exceed the speed of light?

No, the momentum of a relativistic particle can never exceed the speed of light. This is because as the particle's speed approaches the speed of light, its mass increases and it requires an infinite amount of energy to accelerate it any further.

4. How does the momentum of a relativistic particle affect its energy?

The momentum of a relativistic particle is directly related to its energy through the equation E = √(p^2c^2 + m^2c^4), where E is the energy, p is the momentum, m is the mass, and c is the speed of light. As the momentum increases, so does the energy of the particle.

5. In what units is momentum of a relativistic particle typically measured?

The momentum of a relativistic particle is typically measured in units of kilogram meters per second (kg·m/s) or electron volts per speed of light (eV/c). These units take into account the effects of special relativity and allow for easier comparison between particles of different masses and speeds.

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