What is the speed of the proton?

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The speed of a proton accelerated from rest through a 50 million volt potential difference can be calculated using energy equations. The charge of the proton is equivalent to that of an electron, at approximately 1.6 x 10^-19 coulombs. Initial calculations using the classical kinetic energy formula yield a speed of about 1 x 10^8 m/s, which approaches relativistic speeds. Therefore, the relativistic kinetic energy equation should be applied instead of the classical one for accurate results. Ensuring the correct mass of the proton, which is 1.67 x 10^-27 kg, is crucial for the calculations.
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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?
 
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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.
 


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


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


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.
 


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.
 

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