Stationary particle decay into two particles with DIFFERENT masses

In summary, the conversation is about finding the energies and speeds of two fragments that result from the decay of a particle with a mass of 7m. The solution involves using conservation of energy and momentum equations, as well as the energy-momentum invariant. The final solution is achieved by using the conservation of momentum equation and solving for the velocities.
  • #1
mmh37
59
0
I have been thinking and thinking this over, but I just can't find the solution - can anyone help?
A particle of mass 7m which is initially at rest in the laboratory frame decays into two fragments whose rest masses are 2m and 3m. Find the energies of the fragments and their speeds in the lab frame.
Help's much appreciated!
 
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  • #2
Well, energy will be conserved, as will momentum. So you can calculate their total energy by using E = mc^2, and then you can use conservation of momentum as well, and then you have two equations with two unknowns. Solve.
 
  • #3
That's what I've been trying to do:

conservation of energy: 7mc^2 = gamma(1)*2mc^2 + gamma(2)*3m^2

(different gamma factors as the particles move with different velocities)

conservation of momentum:

0 = gamma(1)*2m*v1 + gamma(2)*3m*v2


Then you end up with a very unpleasant equation, which I cannot solve.

Does anyone know how to do so or whether there is an easier way (which I'm sure has to exist). I've also tried to work with the energy momentum invariant and different frames of reference (which doesn't make any sense at all here, but I wanted to give it a go anyway).
 
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  • #4
well, as far as i can remember the quantity [tex]\sqrt{m^2c^4+p^2c^2}[/tex] is conserved.
so [tex]7mc^2=\sqrt{9m^2c^4+4m^2c^4+p_1^2c^2+p_2^2c^2}[/tex]
and the momentum is conserved too, so [tex]p_1=-p_2[/tex]
and i think you can find the different velocities by [tex]\gamma_1 3mv=p_1[/tex]
and [tex]\gamma_2 2mv=p_2[/tex]
 
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  • #5
:rofl: thanks for your help!
It now works! :smile:
 

1. What is stationary particle decay into two particles with different masses?

Stationary particle decay into two particles with different masses is a type of particle decay process in which a single, stationary particle breaks apart into two separate particles with different masses.

2. How does this type of decay occur?

This type of decay occurs through the weak nuclear force, which is one of the four fundamental forces of nature. It is a random process and cannot be predicted exactly when it will occur.

3. What are the two particles that result from this decay?

The two particles that result from this decay can vary, but they are typically a lighter particle and a heavier particle. Examples include a neutron decaying into a proton and an electron, or a muon decaying into an electron and two neutrinos.

4. What happens to the energy and momentum of the original particle?

The total energy and momentum of the original particle are conserved in this process. This means that the sum of the energies and momenta of the two resulting particles is equal to the energy and momentum of the original particle.

5. Why is this type of decay important in particle physics?

This type of decay is important in particle physics because it provides insight into the fundamental nature of particles and their interactions. By studying the properties of the resulting particles, scientists can gain a better understanding of the underlying laws of the universe.

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