# Kinetic energy of electrons/protons

Hi, I'm working on the following:

An electron starting from rest acquires 6.3 keV of KE in moving from point A to point B. (a) How much KE would a proton acquire, starting from rest and moving to point A? (b) Determine the ratio of their speeds at the end of their respective trajectories.

So I understand that the proton will also have a KE of 6.3 keV because it has an equal but opposite charge to the electron (part A). But could someone give me a hint about the whole ratio of speeds part? Would I use some equation for velocity, and if so, how would I use the keV in it? Or do I use the respective masses of electrons and protons? Thx.

Use the relativistic equation

$$E = \gamma m c^2$$

where m is the rest mass to find the velocities of e and p.

The equation for kinetic energy is

$$KE = \frac{1}{2} m v^2$$

using conservation of energy, how would the KE of the electron compare to the KE of the proton?

edit: This is assuming your looking at it from the "classical" sense. If not, look to the post above

dextercioby
Homework Helper
There's no need for relativistic formula,the ratio is approx 1/100 for the electron and 1/180000 for the proton (if the latter has the same 6.3 KeV).

Daniel.

I'm sorry Dexter, I don't think I understand what you're saying?? The answer, according to my friend, is something like 1:43. So I am looking for the ratio of their two velocities. This is dependent on mass, correct? Thanks.

Andrew Mason
Homework Helper
thisisfudd said:
An electron starting from rest acquires 6.3 keV of KE in moving from point A to point B.
Are we to assume that it acquires this KE by passing through an electric field? There are other ways it can acquire kinetic energy.

AM

dextercioby
Homework Helper
thisisfudd said:
I'm sorry Dexter, I don't think I understand what you're saying?? The answer, according to my friend, is something like 1:43. So I am looking for the ratio of their two velocities. This is dependent on mass, correct? Thanks.

I was making the ratio:
$$(\frac{KE}{Rest \ mass \times c^{2}})_{electron} \sim \frac{6.3KeV}{511KeV}\sim \frac{1}{85}$$

Well,i approximated (not too accurately,though) to 1/100 and called the use of relativistic energy formula a mere complication...

Daniel.

xanthym
thisisfudd said:
Hi, I'm working on the following:

An electron starting from rest acquires 6.3 keV of KE in moving from point A to point B. (a) How much KE would a proton acquire, starting from rest and moving to point A? (b) Determine the ratio of their speeds at the end of their respective trajectories.

So I understand that the proton will also have a KE of 6.3 keV because it has an equal but opposite charge to the electron (part A). But could someone give me a hint about the whole ratio of speeds part? Would I use some equation for velocity, and if so, how would I use the keV in it? Or do I use the respective masses of electrons and protons? Thx.

SUMMARY OF ESTABLISHED PROBLEM ITEMS:

$$:(1): \ \ \ \ (ElectronKineticEnergy) = (ProtonKineticEnergy) = (6.3 keV)$$

$$:(2): \ \ \ \ \frac { M_{electron} V^{2}_{electron} } {2} = \frac { M_{proton} V^{2}_{proton} } {2} = (6.3 keV)$$

{Electron Mass} = (9.1093897e-31 kg)
{Proton Mass} = (1.6726231e-27 kg)

~~