Modern Physics question -- an atom ejecting a relativistic electron

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SUMMARY

The discussion revolves around calculating the speed of an atom that ejects a relativistic electron in a particle accelerator. Using the equation u0 x =(ux −v )/(1−uxv/c^2), where ux is the maximum speed of the ejected electron (0.5c) and v is the observed speed (0.75c), the initial calculation yielded -0.4c. However, the correct interpretation reveals that the atom must be moving at a speed of 0.4c, after addressing the sign issue in the calculation. This highlights the importance of careful setup and verification in relativistic physics problems.

PREREQUISITES
  • Understanding of relativistic velocity addition
  • Familiarity with the equation u0 x =(ux −v )/(1−uxv/c^2)
  • Basic knowledge of radioactive decay processes
  • Concept of relativistic speeds (e.g., speeds approaching the speed of light)
NEXT STEPS
  • Study the principles of relativistic velocity addition in detail
  • Explore examples of radioactive decay and its implications in particle physics
  • Learn how to verify calculations in relativistic contexts
  • Investigate the effects of speed on particle behavior in accelerators
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Students of physics, particularly those studying particle physics and relativistic mechanics, as well as educators looking for examples of problem-solving in advanced physics topics.

Dan350
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Homework Statement

.
An atom at rest can undergo radioactive decay, ejecting an electron at a maximum speed of 0.5c. If the atom in a particle accelerator is observed to produce an electron traveling at 0.75c, at least how
fast must the atom itself have been moving?

Homework Equations


u0 x =(ux −v )/(1−uxv/c^2)

The Attempt at a Solution


The problem is asking for the speed of the atom,

I set
ux=0.5c
v=0.75
After plugin in, I get the result of -0.4c

I don't feel sure aboout this anwser.
Any suggeestions? Corrections?
 
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Dan350 said:

Homework Statement

.
An atom at rest can undergo radioactive decay, ejecting an electron at a maximum speed of 0.5c. If the atom in a particle accelerator is observed to produce an electron traveling at 0.75c, at least how
fast must the atom itself have been moving?

Homework Equations


u0 x =(ux −v )/(1−uxv/c^2)

The Attempt at a Solution


The problem is asking for the speed of the atom,

I set
ux=0.5c
v=0.75
After plugin in, I get the result of -0.4c

I don't feel sure aboout this anwser.
Any suggeestions? Corrections?

You just have to sort out the minus sign!
 
PeroK said:
You just have to sort out the minus sign!
So the awnser is simply 0.4c?
 
Dan350 said:
So the awnser is simply 0.4c?
What you didn't do was set the problem up in any meaningful way. Why did you use the equation you did? Can you not check an answer of 0.4c yourself?
 

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