Find the final speed of an electron

In summary, the final speed of an electron passing between two parallel plates with a potential difference of 5000V can be calculated using the equation v = √[2qV/m]. Using the given values of q = 1.6*10^-19C and m = 9.1*10^-31kg, the final speed is found to be 4.2*10^7 m/s. However, this calculation does not account for the mass increase of the electron as it approaches the speed of light, which may lead to invalid results for higher potential differences.
  • #1
marshall4
50
0
Find the final speed of an electron, starting from rest, passing between two parallel plates with a potential difference of 5000V.

m=9.1*10^-31kg
q=1.6*10^-19C

v=sqr root of [2(1.6*10^-19)(5000)]/9.1*10^-31 = 4.2*10^7 m/s

Is this answer valid, why?
 
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  • #2
Yes and No

The calculation is correct and in Classical Physics all is fine. However, if you increase the PD to say 30,000V you will find the electron traveling faster than the speed of light!

Your calculation doesn't account for the mass increase of the electron as it approaches the speed of light. For most School work it is fine though.
 
  • #3


Yes, this answer is valid. The final speed of an electron can be calculated using the equation v=sqrt(2qV/m), where q is the charge of the electron, V is the potential difference, and m is the mass of the electron. Plugging in the given values for q, V, and m, we get a final speed of 4.2*10^7 m/s. This answer is valid because it follows the correct formula and uses the correct unit conversions. Additionally, the calculated speed is within a reasonable range for the speed of an electron in this scenario.
 

1. How can I calculate the final speed of an electron?

To calculate the final speed of an electron, you will need to know the initial speed of the electron, the force acting on the electron, and the distance the electron travels. You can use the equation v^2 = u^2 + 2as, where v is the final speed, u is the initial speed, a is the acceleration (determined by the force acting on the electron), and s is the distance traveled.

2. What is the initial speed of an electron?

The initial speed of an electron can vary depending on the source of the electron. For example, in a cathode ray tube, the initial speed of the electron is typically around 10^7 meters per second.

3. What is the force acting on an electron?

The force acting on an electron can also vary depending on the situation. In an electric field, the force acting on an electron is given by the equation F = Eq, where E is the electric field strength and q is the charge of the electron. In a magnetic field, the force acting on an electron is given by the equation F = Bqv, where B is the magnetic field strength and v is the velocity of the electron.

4. What is the distance an electron travels?

The distance an electron travels can also vary depending on the situation. In a vacuum, an electron can travel for a very long distance without experiencing significant resistance. In other situations, the distance may be limited by obstacles or other forces acting on the electron.

5. Can I use this equation to calculate the final speed of any particle?

Yes, this equation can be used to calculate the final speed of any particle, as long as you have the necessary information such as initial speed, force, and distance traveled. However, the equation may need to be modified for particles with different properties, such as mass or charge.

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