Relativity with energy and momentum question

AI Thread Summary
The discussion centers on a physics problem involving a pi meson with a rest mass of 131 MeVc-2 and a total energy of 1.000 GeV. The user successfully calculated the momentum as 991 MeVc-1 and determined that the speed is 2.57x10^6 ms-1 less than the speed of light. However, they are struggling with part c, which involves finding the maximum and minimum energies of two photons resulting from the meson's decay. The user notes that while the decay is symmetric in the rest frame of the pion, it becomes asymmetric in the lab frame, leading to different energies for the photons due to momentum conservation. The discussion highlights the complexity of applying the Doppler effect to this scenario and the need for a deeper understanding of energy distribution in relativistic decays.
StonedPhysicist
Messages
25
Reaction score
0
Here is the question, I was able to complete part a and b but c has beaten me!

A pi meson has rest mass 131 MeVc-2 and total energy 1.000 GeV

a) What is its momentum, expressed in MeVc-1
For this I obtained 991 MeVc-1 using the equation E2=c2p2+M2c4

b) By how much is its speed less than c?
Using γ=E/mc2 i got a value of γ = 7.63 so therefore this system is highly relativistic then subbed this into γ=1/√(1-v2/c2) to get an answer of 2.57x106 ms-1 less than c.

c) This is the one i am stuck on: The pi meson decays in flight into two photons. Find the maximum and minimum energies (in MeV) possible for the photons in the coordinate system (or reference frame) of the observer who measures this total energy, and the minimum and maximum wavelengths corresponding to these energies.

I do not quite understand what it means by or how to get the maximum and minimum energies. I would of assumed both photons get half the total energy and half the total momentum each.


 
Physics news on Phys.org
In the rest frame of the pion, the decay is symmetric, but in the lab frame (where the pion is moving) it can be asymmetric. The two photons can have different angles relative to the pion flight direction.
 
mfb said:
In the rest frame of the pion, the decay is symmetric, but in the lab frame (where the pion is moving) it can be asymmetric. The two photons can have different angles relative to the pion flight direction.

I don't see how this will give them different energies though?
 
could it be a doppler effect?
 
StonedPhysicist said:
I don't see how this will give them different energies though?
Imagine one flying in the pion flight direction and one backwards. If they would have the same energy and momentum, total momentum would be zero after the decay but non-zero before. A violation of momentum conservation.

It is related to the Doppler effect, but formulas for that are impractical here.
 
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Correct statement about a reservoir with an outlet pipe'
The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...

Similar threads

Replies
4
Views
2K
Replies
2
Views
948
Replies
15
Views
4K
Replies
1
Views
1K
Replies
6
Views
2K
Replies
3
Views
1K
Back
Top