What Voltage Accelerates an Electron Over 0.350 m in 46.0 ns?

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Homework Help Overview

The problem involves calculating the voltage required to accelerate an electron over a distance of 0.350 m in a time frame of 46.0 ns. The context is rooted in concepts of kinetic energy and electric potential energy, particularly in relation to charged particles in motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between velocity, kinetic energy, and voltage. Some express uncertainty about the correct equations to use, while others attempt to derive the final velocity and kinetic energy of the electron. Questions about the assumptions regarding initial conditions and the nature of acceleration are also raised.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have suggested using the kinetic energy formula and the relationship between electric potential and energy. There is acknowledgment of the need to consider the electron's acceleration rather than assuming constant velocity, and participants are encouraged to show their work for further analysis.

Contextual Notes

Participants note the importance of understanding the initial conditions of the electron's motion, including its initial velocity and the mass of the electron. There is also mention of the need to clarify the units of energy being discussed, particularly in relation to electron volts.

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Homework Statement



If an electron travels 0.350 m from an electron gun to a TV screen in 46.0 ns, what voltage was used to accelerate it? (Note that the voltage you obtain here is lower than actually used in TVs to avoid the necessity of relativistic corrections.)



Homework Equations



E=k(q/r^2) ΔV=|Ed| ΔKE + ΔPE = 0

The Attempt at a Solution



I have no clue how to answer this question. I don't know if it's because I am trying to use the wrong equations, or because I am just not seeing the connections
 
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If the electron travels 0.35 m in 46 ns, what velocity does it travel at? Hence what KE does it posses at this velocity? Also how does voltage and charge relate to energy?
 
If the electron travels 0.35 m in 46 ns, what velocity does it travel at? Hence what KE does it posses at this velocity? Also how does voltage and charge relate to energy?

Well the velocity is going to be at about 7.6x10^6 m/s. I know that K.E.= 1/2mv^2, so can I calculate the kinetic energy of that and use it as the energy to calculate voltage? I am a little lost
 
Keep in mind that the electron will be accelerating throughout its journey; It doesn't cover the interval at a constant speed.

What's the formula for the energy gained by a charged particle falling through a given potential difference?
 
E = |qΔV|? is that the equation you are talking about?
 
Shinster007 said:
E = |qΔV|? is that the equation you are talking about?

Yes.
 
Well the only thing that I can think of using is the Δ Kinetic Energy + Δ Electric Potential=0 and then trying to solve for V (voltage).
 
Shinster007 said:
Well the only thing that I can think of using is the Δ Kinetic Energy + Δ Electric Potential=0 and then trying to solve for V (voltage).

Sounds like a good plan :wink:
 
Ha ha okay, I actually tried doing that earlier but I got the wrong answer. Which of the Velocities and voltages are zero? And for the mass of the electron do I use 9.1X10^-31?
 
  • #10
Shinster007 said:
Ha ha okay, I actually tried doing that earlier but I got the wrong answer. Which of the Velocities and voltages are zero? And for the mass of the electron do I use 9.1X10^-31?

Show your work so we can see where something might have gone wrong.

The electron starts out with zero velocity and accelerates to the screen thanks to the potential difference.
 
  • #11
1.)1/2m(Vf^2-Vi^2) + q(Vf-Vi)=0, cancel out initial velocity and final voltage (I think) since they are zero.
2.)1/2mVf^2-qV=0
3.) 1/2mVf^2=qV
4.)1/2mVf^2/q=V

That's what I tried, and got the wrong answer so I guess that I am setting up the equation wrong.
 
  • #12
m=mass of electron, 9.1x10^-31 kg
Vf= 7.61x10^6
q= 1.6x10^-19

Those are the numbers I am using
 
  • #13
Shinster007 said:
m=mass of electron, 9.1x10^-31 kg
Vf= 7.61x10^6
q= 1.6x10^-19

Those are the numbers I am using

How did you determine Vf? Remember that the electron is undergoing accelerated motion, not constant velocity...
 
  • #14
Hmmm that is true. I am kinda stumped then
 
  • #15
How did you get this Velocity ?

I think you have erred in calculating the Final Velocity at x=0.35m
 
  • #16
Shinster007 said:
Hmmm that is true. I am kinda stumped then

It's just the usual accelerated motion of a projectile. Use the information given (distance and time) to find the final velocity assuming that a constant acceleration is applied. Hint: you can begin by determining the acceleration.
 
  • #18
Okay, I will try to figure it out. In the meantime, can you help me with another question?


The problem is as follows:


In nuclear fission, a nucleus splits roughly in half.

(a) What is the potential 3.50 10-14 m from a fragment that has 50 protons in it?
I calculated this to be 2.05x10^6, which is correct.


(b) What is the potential energy in MeV of a similarly charged fragment at this distance?

I have no idea what this part is asking for; our professor did not go over those units at all and the textbook we are using is very vague on the subject.
 
  • #19
Shinster007 said:
Okay, I will try to figure it out. In the meantime, can you help me with another question?


The problem is as follows:


In nuclear fission, a nucleus splits roughly in half.

(a) What is the potential 3.50 10-14 m from a fragment that has 50 protons in it?
I calculated this to be 2.05x10^6, which is correct.


(b) What is the potential energy in MeV of a similarly charged fragment at this distance?

I have no idea what this part is asking for; our professor did not go over those units at all and the textbook we are using is very vague on the subject.

eV stands for 'electron volt'. It's a unit of energy equivalent to the energy gained by a unit electric charge (the magnitude of the charge on the electron) falling through a potential difference of 1 volt. Hence electron volt.

MeV is Mega eV, that is, a million eV.
 
  • #20
Okay, so how can I go from the volts to ev?
 
  • #21
Shinster007 said:
Okay, so how can I go from the volts to ev?

First you'll have to determine the potential energy of the second fragment at the stated location. You know its charge and the potential at the given distance. Convert the resulting energy value (Joules) to eV.
 

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