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Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be $1.67 \times 10^{-27} \mathrm{kg}$

$\frac{v_{e}}{v_{H}}=42.8$

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

Simon Fraser University

University of Sheffield

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All right, so in this problem, we have two particles. Ah, why is electron and the otherwise hydrogen Valium? So? So this is the electron. And this is the hydrogen Iram Ah. Which has negative charge. And ah, the mess is, uh, damage equal, man Pole. Oh, sorry. 1.67 times. 10 to the negative 27th kilogram. And the mess off the electron is ah, 9.1 times 10 to the negative. 31 kilograms. Okay, so suppose these two particles dear through the saying voltage. And we want to compare their ah, their voltage there their speed so we can utilize energy conservation law. We see that half because this is, ah, low energy case. So we didn't consider the relativistic effect. So we have the energy expression off and V squared equal Q times V Right. So this this movie and this one's capital B. Okay, so small V is the velocity all army and the speed of this particle and the capital is the body of difference. And for the different particles we have for different labels. So for the electron, we have this as the and this is sorry. This is security And this is Sammy. And before the ah, for the hydrated iron, we have half damage. VH squared equal. Qh comes Meet Ray. And because from the problem, we don't know that Ah, the Hydra alien has this in charge, as the electrons and the mess difference are the message they're giving away here so we can see that. Sami B squared divide by damage, VH Squid equal one. Right. And then we're gonna resolve the ratio of the speed between this two particles. So the over the H equal square roots mh over. I mean, right. So the images but here and enemies over here, So you can just do the calculation. And the video is Ah, 42 0.8. Yeah.

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