What Is the Speed of an Electron With 100000 eV Kinetic Energy?

In summary, to find the speed of an electron with a kinetic energy of 100000 eV, we can use the equations m=m0/√(1-β2) and K=Δmc2. After plugging in the given values and simplifying, we get a velocity of 0.9*108 m/s. However, the correct answer according to the textbook is 1.6*108 m/s. It is likely that the error occurred while plugging in the numbers and evaluating the equation.
  • #1
RubinLicht
132
8

Homework Statement


what is the speed of an electron with kinetic energy of (a) 100000 eV

Homework Equations


m=m0/√(1-β2)
K=Δmc2

The Attempt at a Solution


plug first into second equation, isolate v and it eventually comes out to be
v=c(1-(1+K/m0c2)-2)
plug in numbers and i get a velocity of 0.9*108 m/s
the answer is 1.6*108 m/s in the textbook.

Note: This isn't a school assignment. I am self studying for physics olympiad, and this is my first encounter with relativity from a mathematical stand point.
 
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  • #2
Your method is correct. So, the mistake must be in plugging in the numbers and evaluating.
 
  • #3
will try again, thanks
 

FAQ: What Is the Speed of an Electron With 100000 eV Kinetic Energy?

1. What is the relationship between an electron's kinetic energy and its velocity?

The kinetic energy (KE) of an electron is directly proportional to its velocity. This means that as the electron's velocity increases, its kinetic energy also increases.

2. How can the velocity of an electron be calculated from its kinetic energy?

The velocity of an electron can be calculated using the formula v = √(2KE/m), where v is the velocity, KE is the kinetic energy, and m is the mass of the electron.

3. Can an electron's velocity ever exceed the speed of light?

No, according to Einstein's theory of relativity, the speed of light is the maximum speed at which any object can travel. Therefore, an electron's velocity cannot exceed the speed of light.

4. How does the temperature of a material affect the velocity of its electrons?

The temperature of a material affects the velocity of its electrons because as the temperature increases, the average kinetic energy of the particles in the material also increases. This results in an increase in the velocity of the electrons.

5. Is there a limit to how fast an electron can travel?

Yes, according to the laws of physics, there is a limit to how fast an electron can travel. This limit is the speed of light, which is approximately 299,792,458 meters per second in a vacuum.

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