Modern Physics question -- an atom ejecting a relativistic electron

In summary, the problem is asking for the speed of the atom based on the observed speed of an electron ejected during radioactive decay. Using the given equation, the speed of the atom can be calculated by setting the speed of the ejected electron (ux) to 0.75c and solving for the atom's speed (u0). The resulting answer is -0.4c, but this is not a physically possible solution. The correct answer is 0.4c.
  • #1
Dan350
44
0

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?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
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!
 
  • #3
PeroK said:
You just have to sort out the minus sign!
So the awnser is simply 0.4c?
 
  • #4
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?
 

Related to Modern Physics question -- an atom ejecting a relativistic electron

1. What is the definition of a relativistic electron?

A relativistic electron is an electron that is moving at a significant fraction of the speed of light. This means that the electron's kinetic energy is comparable to its rest mass energy, and therefore, its behavior is governed by the principles of special relativity.

2. How does an atom eject a relativistic electron?

An atom can eject a relativistic electron through a process called electron emission. This can occur through various mechanisms such as photoemission, where the electron absorbs a photon and gains enough energy to escape the atom's surface, or through impact ionization, where the electron gains enough energy from a collision with another particle to leave the atom's vicinity.

3. What is the significance of a relativistic electron in modern physics?

Relativistic electrons play a crucial role in many modern physics phenomena, such as particle accelerators, nuclear reactions, and quantum field theory. They also have practical applications in technologies such as electron microscopy and radiation therapy.

4. Can an atom eject multiple relativistic electrons at once?

Yes, an atom can eject multiple relativistic electrons at once through processes such as Auger electron emission. This occurs when an inner shell electron is ejected from the atom, causing an outer shell electron to fill the vacant spot. The energy released in this process can then eject another outer shell electron with high energy.

5. How does the ejection of a relativistic electron affect the atom's stability?

The ejection of a relativistic electron can destabilize the atom, causing it to become ionized or undergo nuclear reactions. This is because the atom has lost an electron, changing its charge and potentially altering its chemical and physical properties. In some cases, the atom may also emit radiation as it tries to regain stability.

Similar threads

Modern Physics-Einstein's Postulates/Relativistic Velocity
    • Introductory Physics Homework Help
Replies
6
Views
3K
How Does Changing the Work Function Affect Photoelectron Emission?
    • Introductory Physics Homework Help
Replies
4
Views
2K
Modern Physics Introduction Question on Electron Speed and Momentum
    • Introductory Physics Homework Help
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top