How long after the decay do ##e^{-}## and ##e^{+}## Collide

  • Thread starter Potatochip911
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In summary, a type of fundamental particle decays into an electron and a positron in the presence of a uniform magnetic field. The time it takes for the electron and positron to collide after the decay can be found using the equation T=2πme/qB, where T is the period, me is the mass of the electron, q is the charge, and B is the magnitude of the magnetic field. While it may seem that they would collide at T, the solutions manual states that they collide at T/2, which may be due to the fact that the particles are moving in opposite directions.
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Potatochip911
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Homework Statement


A particular type of fundamental particle decays by transforming into an electron ##e^{-}## and a positron ##e^{+}##. Suppose the decaying particle is at rest in a uniform magnetic field of magnitude 3.53 mT and the ##e^{-}## and ##e^{+}## move away from the decay point in paths lying in a plane perpendicular to the magnetic field. How long after the decay do the ##e^{-}## and ##e^{+}## collide?

Homework Equations



The Attempt at a Solution



The period which is all we need to solve this problem can be found to be ##T=\frac{2\pi m_{e}}{qB}## for this problem. Personally I think these particles would collide at ##t=T## but in the solutions manual it says they collide at ##t=T/2##. This doesn't entirely make sense to me since although both the particles are moving at a speed ##v## they won't have completed the entire rotation at ##T/2## although they will have traveled a total distance ##2\pi r##
 
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Maybe I'm missing something, but won't they collide after each has gone half way around the circle?
 
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haruspex said:
Maybe I'm missing something, but won't they collide after each has gone half way around the circle?
I understand the path they take now. I assumed that both electrons were traveling in the same direction at the start, in this case it will be T before they collide. But if the angle between the two speeds is 180 then it only takes T/2.
 

Related to How long after the decay do ##e^{-}## and ##e^{+}## Collide

1. How is the decay of ##e^{-}## and ##e^{+}## related to their collision?

The decay of ##e^{-}## and ##e^{+}## is directly related to their collision. When a particle decays, it produces other particles, including ##e^{-}## and ##e^{+}##. These particles have opposite charges, so they are attracted to each other and will eventually collide.

2. How long does it take for ##e^{-}## and ##e^{+}## to collide after the decay?

The time it takes for ##e^{-}## and ##e^{+}## to collide after the decay depends on the specific decay process and the distance between the particles. Generally, it can range from a few nanoseconds to several milliseconds.

3. What factors can affect the timing of the collision after decay?

The timing of the collision after decay can be affected by several factors, including the energy of the particles, the strength of their electric charges, and the distance between them. Other external factors, such as magnetic fields, can also have an impact.

4. Is there a way to predict when the collision between ##e^{-}## and ##e^{+}## will occur after decay?

Yes, scientists use mathematical models and equations to predict the timing of the collision between ##e^{-}## and ##e^{+}## after decay. These models take into account various factors, such as the particles' energies and charges, to make accurate predictions.

5. What happens after ##e^{-}## and ##e^{+}## collide after decay?

After the collision between ##e^{-}## and ##e^{+}##, the particles can either annihilate each other and produce other particles or scatter off in different directions. The specific outcome depends on the energy and other properties of the particles involved.

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