Finding the energies of 2 photons from a decay of a travelling mass

In summary, a moving mass M at v=c/3 decays into two photons in opposite directions. This mass M was originally formed by a mass m traveling at v=3c/5 and hitting a stationary mass m. This results in M v=c/3 and M=3m/√2. To find the ratio of the energies of the photons, use the formula E^2 - p^2c^2 = m^2c^4 and set m=0. Then, set up simultaneous equations to find the relationship between the energy and momentum of each photon. However, the intermediate step provided in the conversation may not be correct as it does not conserve energy and momentum.
  • #1
Aaron7
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0

Homework Statement


Mass M traveling at v=c/3 decays into 2 photons in x and -x directions.

Mass M orginally formed by mass m traveling at v=3c/5 hitting a stationary mass m.
This gives M v=c/3 and M=3m/√2.

Homework Equations



E=K + mc^2

p = gamma m v
E = gamma m c^2

K = (gamma -1) mc^2

E^2 - p^2 c^2 = m^2 c^4

The Attempt at a Solution



I am confused how the photons form from a moving mass. How would I find out the ratio of the energies of the photons?
 
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  • #2
Use your E2 - p2c2 = m2c4 formula to find the relationship of a given photon's momentum and its energy. Set m = 0. Then solve for p.

Then set up the following simultaneous equations (noting that the photons fly off in opposite directions on the x-axis):
  • (Energy of one photon) + (Energy of the other photon) = (The original energy of the system)
  • (|Momentum of one photon|) - (|Momentum of the other photon|) = (|Original momentum of the system|)

"Original energy of the system" above is the original total energy of the system; not just its kinetic energy. You have two equations and two unknowns. You can take it from there.
Aaron7 said:
Mass M orginally formed by mass m traveling at v=3c/5 hitting a stationary mass m.
This gives M v=c/3 and M=3m/√2.
Your above calculations kinda worry me. Is this intermediate step something you are explicitly told to calculate? If so, I don't think it's correct: According to my calculations, (total) energy and momentum are not conserved in your calculations (as they should be). If you are not required to perform this intermediate step, then I don't think it's necessary.
 
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What is the process of finding the energies of 2 photons from a decay of a travelling mass?

The process involves using the principles of conservation of energy and momentum to calculate the energies of the photons. This can be done by analyzing the decay products of the travelling mass and using equations such as E=mc^2 and p=mv.

How do you determine the energies of the photons in such a decay?

The energies of the photons can be determined by measuring their wavelengths or frequencies, as well as considering the masses and velocities of the particles involved in the decay. These values can then be used in the equations E=hc/λ or E=hf to calculate the energies.

What factors can affect the energies of the photons in this type of decay?

The energies of the photons can be affected by the mass and velocity of the travelling mass, as well as any interactions or collisions with other particles during the decay process. Additionally, the direction and angle of emission of the photons can also impact their energies.

Is it possible to calculate the energies of the photons accurately?

Yes, it is possible to calculate the energies of the photons accurately using the principles of conservation of energy and momentum. However, there may be uncertainties or errors in the measurements of the decay products that can affect the accuracy of the calculations.

What is the importance of finding the energies of the photons in this type of decay?

Finding the energies of the photons can provide important information about the properties and interactions of particles involved in the decay process. This can help further our understanding of fundamental laws and principles in physics, and also has practical applications in fields such as medical imaging and energy production.

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