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Unreasonable Results(a) What is the final speed of an electron accelerated from rest through a voltage of 25.0 MV by a negatively charged Van de Graaff terminal?(b) What is unreasonable about this result?(c) Which assumptions are responsible?

(a) $v_{f}=2.96 \times 10^{9} \mathrm{m} / \mathrm{s}$(b) The final speed of the electron is greater than the speed of light $(3.0 \times\left.10^{8} \mathrm{m} / \mathrm{s}\right)$ which is impossible.(c) The accelerating voltage is so great, therefore, we should have used the relativistic approach to calculate the final speed of the electron.

Physics 102 Electricity and Magnetism

Chapter 19

Electric Potential and Electric Field

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

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All right, so in this problem, we're accelerating electrons through the violent Graaff accelerator. So, uh, we know the potential difference of this vent A graph terminal is Ah, that would be equal 25 mega volts. So the phone energy that this election, I can say is ah e equal that heavy times e ray, and this gives you 25 mega ultra votes. So if we use the traditional Newton ah interpretation to find out the the the speed that this ah, electric and rich we can we can list the question half and times V squid equal the total energy right which is right here. So am is the mass of the electron and find out of the velocity by this myself in this equation and you will see that the velocity equal 2.96 times 10 to the ninth meters per second. So there's a party and Herbie So why this result is not reasonable. That's because this velocity is too large, right, because the speed of light is actually ah, the physical maximum velocity that we can rich. So that's be these three times 10 to the eighth meters a second and as you can see that these laws that is much larger than this one. Right? So this is not reasonable. And, Percy, why this is no reasonable. That's because we're using the Newton interpretation to list to find out the velocity of this. Ah, electoral. That's actually not ah, correct here because this e I mean, because the potential difference off this vent vent a graph terminal is too large so that we can not to use the Newton kind energy to find up to the velocity we have the unit, I would have to consider the relativistic effect. So we basically just ignored relativistic relativistic effect. So that's why this is not reasonable.

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