''Invariant mass of the electron and electron antineutrino''

In summary: The invariant mass of a system consisting of two particles is the norm of the four-momentum of that system.
  • #1
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1. A neutron decays into a proton, an electron and an electron antineutrino. In the frame of the neutron, the proton is in rest after decay. Calculate the ''invariant mass of the electron and electron antineutrino together''. The rest masses of the proton and neutrno are known2. Conservation of energy, momentum and conservation of four momentum.

3. The problem is that I don't understand what is asked of me, are they asking for ##m_{e} + m_{v}##? If so, I start like this in natural units (h bar = 1 , c=1)

##m_{n}=m_{p} + E_{e} + E_{v}##

Plugging in the relativistic formulas for energy, and knowing that since the proton has no momentum the momenta of the electron and antineutrino have to be equal in size:

##\sqrt{p^{2}+m_{e}^{2}}+\sqrt{p^{2}+m_{v}^{2}}=m_{n}-m_{p}##

Seems like not enough info, hence I'm doubting I'm correctly interpreting the question.
 
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  • #2
They are asking for the "invariant mass of the electron and electron antineutrino together". That is, they are asking the invariant mass of a system consisting of those two particles. That is not the same thing as asking for the sum of the invariant mass of the electron of the electron anti-neutrino.
 
  • #3
jbriggs444 said:
They are asking for the "invariant mass of the electron and electron antineutrino together". That is, they are asking the invariant mass of a system consisting of those two particles. That is not the same thing as asking for the sum of the invariant mass of the electron of the electron anti-neutrino.

Is ## \sqrt{ (p_{e} + p_{v})^{2}}## the correct interpretation then? Where ##p_{e}## and ##p_{v}## represent the four momenta of the particles?
 
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  • #4
When it comes to four-momentum, I am out of my depth, and am working from first principles. But no, that does not appear to be the correct interpretation.

Edit: It looks correct now.

Go back to definitions. What is the definition of invariant mass of X? The norm of the four-momentum of X, right? So if X is a system consisting of two particles...
 
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  • #5
jbriggs444 said:
When it comes to four-momentum, I am out of my depth, and am working from first principles. But no, that does not appear to be the correct interpretation.

Go back to definitions. What is the definition of invariant mass of X? The norm of the four-momentum of X, right? So if X is a system consisting of two particles...

Oh damn I messed up my squares being too qucik, here I fixed it. What about now?
 
  • #6
Yes, that works.
 

Related to ''Invariant mass of the electron and electron antineutrino''

What is the invariant mass of the electron and electron antineutrino?

The invariant mass of the electron and electron antineutrino is the mass that remains constant regardless of the reference frame in which it is measured. It is a fundamental property of these particles and is a key factor in understanding their behavior.

How is the invariant mass of the electron and electron antineutrino calculated?

The invariant mass of the electron and electron antineutrino is calculated using the equation E^2 = (mc^2)^2 + (pc)^2, where E is the energy of the particle, m is its mass, c is the speed of light, and p is its momentum. This equation is derived from Einstein's theory of relativity.

Why is the invariant mass of the electron and electron antineutrino important?

The invariant mass of the electron and electron antineutrino is important because it is a fundamental property that allows us to understand the behavior and interactions of these particles. It is also a key factor in determining the energies and momenta of these particles in various experiments.

How does the invariant mass of the electron and electron antineutrino differ from their rest mass?

The invariant mass of the electron and electron antineutrino is equal to their rest mass when they are at rest, but it remains constant even when they are in motion. This is because the invariant mass takes into account both the rest mass and the kinetic energy of the particles.

Can the invariant mass of the electron and electron antineutrino change?

No, the invariant mass of the electron and electron antineutrino is a fundamental property that remains constant regardless of the reference frame or the energy of the particles. It can only change if the particles undergo a nuclear reaction or decay into other particles.

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