What is the speed of the proton?

In summary: You would need to use the relativistic formula: K = (gamma - 1)mc^2, with gamma = 1/sqrt(1 - v^2/c^2)In summary, the speed of a proton after being accelerated from rest through a 50x106 potential difference can be found using the kinetic energy formula and taking into account relativity. The proton's mass is 1.67x10-27kg and it carries a charge of 1.6x10-19 C. After calculating the energy and plugging it into the kinetic energy formula, a speed of about 1x10^8 m/s is obtained. However, this speed is too close to the speed of light and a more accurate
  • #1
yy205001
60
0
what is the speed of the proton??

Homework Statement


What is the speed of a proton after being accelerated from rest through a 50x106 potential difference?

m_proton = 1.67x10-27kg
C = 1.6x10-19 c
* This question is in Relativity.

Homework Equations


Voltage(v) = Joule(j)/Columb(c)
K = 1/2(mu2)

The Attempt at a Solution


Firstly, i timed 1.6x10-19 to 50x106 to find the Energy(j
). Then plugged into the kinetic energy formula to find u(speed_proton). But which is wrong. what is the mistake?
 
Last edited:
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  • #2


Hi. It seems OK to me. How did you judge you are wrong?
By the way
m_proton = 1.67x106kg is too heavy! -6?, not sure. You should check it in some physics table.
 
  • #3


it should be -27. I was doing a online HW. when i typed in the answer, the system said that it was wrong.
 
  • #4


Does proton carry the same charge as electron??(c=1.6x10^-19)
 
  • #5


If you use KE equation you get a speed of about 1x10^8 m/s...this is a bit too close to the speed of light and you may need to use relativity equation.
 
  • #6


yy205001 said:
* This question is in Relativity.

Homework Equations



K = 1/2(mu2)
If the speed is relativistic, then that is not the correct equation for kinetic energy.
 

FAQ: What is the speed of the proton?

What is the speed of the proton?

The speed of the proton is the measure of how fast a proton is moving in a particular direction. It is a fundamental property of a proton and is an important factor in many scientific studies and experiments.

How is the speed of the proton measured?

The speed of a proton can be measured using various techniques such as particle accelerators, ion traps, and time-of-flight measurements. These methods involve measuring the distance traveled by the proton and the time it takes to cover that distance.

What is the unit of measurement for the speed of the proton?

The speed of the proton is typically measured in meters per second (m/s) or a fraction of the speed of light (c). The speed of light is approximately 299,792,458 m/s, so the speed of the proton is often expressed as a percentage of this value.

What factors can affect the speed of the proton?

The speed of the proton can be affected by various factors such as the presence of magnetic and electric fields, collisions with other particles, and the energy it possesses. The speed can also vary depending on the environment in which the proton is moving.

Why is the speed of the proton important in scientific research?

The speed of the proton is crucial in many areas of scientific research, including particle physics, nuclear physics, and medical imaging. It helps us understand the behavior of subatomic particles and how they interact with each other. Additionally, the speed of the proton is essential in developing technologies such as particle accelerators and medical imaging devices.

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