# Relationship of velocity of an electron/velocity of proton to mass ratio

• sheri1987
In summary, the ratio of the velocity of an electron to that of a proton is given by the equation v_e/v_p = sqrt(-2q_e/q_p) * sqrt(m_p/m_e), where q_e and q_p are the charges of the electron and proton respectively, and m_e and m_p are their masses. This ratio can be obtained by using conservation of energy and solving for the velocities of the two particles.
sheri1987
Relationship of velocity of an electron/velocity of proton to...mass ratio

## Homework Statement

An electron and a proton, starting from rest, are accelerated through an electric potential difference of the same magnitude. In the process, the electron acquires a speed ve, while the proton acquires a speed vp.

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(d) What is the algebraic expression for the ratio ve/vp of the speed of the electron to that of the proton? Express your answer in terms of the mass me of the electron and the mass mp of the proton. (Answer using m_e for me and m_p for mp.)

## Homework Equations

SO I need to write an equation relating Velocity of electron/ velocity of proton...I understand that much...but I am unsure where to start.

I think I need the equation 1/2mv^2 = -q (charge)deltaV(voltage)

## The Attempt at a Solution

by using the equation above I solved and got sqrt(2qdeltaV/m) ...I am not sure where to go next...? Can anyone help me out?

sheri1987 said:
I think I need the equation 1/2mv^2 = -q (charge)deltaV(voltage)

Yes, that's what you want to use.

by using the equation above I solved and got sqrt(2qdeltaV/m) ...I am not sure where to go next...? Can anyone help me out?

Actually, you should get sqrt(-2qdeltaV/m). Then if q<0 (like it is for an electron) then deltaV>0 and the radicand is positive. And if q>0 (like it is for the proton) then deltaV<0, and again the radicand is positive. Just find expressions for the speeds of the proton and the electron, and take their ratio and you'll have it.

sheri1987 said:
by using the equation above I solved and got sqrt(2qdeltaV/m) ...I am not sure where to go next...? Can anyone help me out?
So you have used conservation of energy to almost correctly [note the sign correction] solved for the velocity of a generic particle of charge q and mass m (traveling at non-relativistic speeds). Let me write your equation out in a form that may be easier to work with;

$$v^2 = -2q\Delta V \cdot \frac{1}{m}$$

So now you want that ratio $v_e/v_p$. So you can now write two equations;

$$v_e^2 = -2q_e\Delta V \cdot \frac{1}{m_e}$$

$$v_p^2 = -2q_p\Delta V \cdot \frac{1}{m_p}$$

Can you take the next step?

Edit: Tom beat me to it!

Last edited:

## 1. How does the velocity of an electron compare to its mass ratio?

The velocity of an electron is much greater than its mass ratio. This is because electrons have a very small mass compared to their velocity, which is approximately the speed of light. This means that even small changes in velocity can result in a significant change in the mass ratio of an electron.

## 2. What factors influence the velocity of an electron/proton?

The velocity of an electron or proton is influenced by many factors, such as the strength of an electric or magnetic field, the temperature of the environment, and the presence of other particles. In addition, the mass of the particle itself also plays a role in determining its velocity.

## 3. How is the velocity of an electron/proton measured?

The velocity of an electron or proton can be measured using various techniques, including particle accelerators, mass spectrometry, and spectroscopy. These methods involve manipulating the particles and observing their behavior to determine their velocity and mass ratio.

## 4. What is the significance of the velocity of an electron/proton to mass ratio?

The velocity of an electron/proton to mass ratio is significant because it provides important information about the fundamental properties of these particles. It can also be used to study the behavior of matter and to understand the laws of physics that govern our universe.

## 5. How does the velocity of an electron/proton affect its interactions with other particles?

The velocity of an electron/proton can greatly affect its interactions with other particles. For example, a higher velocity can result in stronger repulsion or attraction between particles, while a lower velocity may lead to weaker interactions. Additionally, the mass ratio of a particle can also impact its interactions with other particles.

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