The ElectronVolt - Online Tutor, Practice Problems & Exam Prep

In the context of electric potential and energy, the electron volt (eV) is a unit representing the change in potential energy of an electron moving through a potential difference of 1 volt. The relationship between potential energy change (ΔU) and potential difference (ΔV) is given by the equation $\mathrm{\Delta U}=q\times \mathrm{\Delta V}$. For kinetic energy calculations, the formula $\mathrm{KE}=1/2mv^2$ is used, where m is mass and v is velocity. Understanding these concepts is crucial for analyzing particle behavior in electric fields.

The ElectronVolt

Hey, guys. So in the last couple of videos, we've talked about electric potentials, and we've talked about electric potential energies. So in this video, we're gonna cover a specific unit that you might run across when talking about these things called the electron volt. Let's check it out. So imagine we have these 2 plates and they're charged, and we have a potential difference of 1 volt across them. So now imagine that we have an electron that starts on the left plate and moves to the right. So I'm gonna drop this little electron right here, and now the charge on that electron is negative e, and this electron wants to move towards the right. Why? Because it wants to go towards higher potentials and it also wants to be attracted towards the positive end of the plate. As this electron is moving between the plates, it is moving through a potential difference, and that potential difference is v, and that's just equal to 1 volt. That's just the difference that we were told. So we have a charge that is moving through a potential difference, and any time that a charge moves through a potential difference, there is a change in potential energy. Remember that those two things are related by the equation ΔU=q⋅ΔV. So that means that we have a charge, which is that negative e, moving through a potential difference, which is 1 volt, and that's just so you can equal negative one e times v. Now all I'd have to do to plug in or to figure out the change in potential energy in joules is just use the relationship that e is the elementary charge, which is 1.6×10−19 joules.

Now what's happening to this potential energy? Well, what's happening is that it is changing from potential to kinetic. So anytime, remember, we have a negative change in potential energy, the potential energy is getting smaller, that means that that's being converted to kinetic energy. As the thing is moving across, it's basically speeding up. Alright? So what if we were to actually have a positive charge? Some of you might be wondering what happens to a positive charge. So basically, what happens is if you have a positive charge, it's gonna do the exact same thing, but backwards. So this positive charge, it wants to go towards the left because it wants to go towards lower potentials and it's attracted to the negative plate that's over here. But now what happens is that the potential difference that it's going through is not 1 volt. We know from the last couple of videos that it's very important that we have positive and negative signs with our potential differences. So if we went to the right and it was positive 1 volt, if we're going to the left, that's actually negative 1 volt. It's final minus initial. So here, this was the initial, and the right side was the final, whereas here, it is backwards. This was my initial, and this is my final. So everything gets sort of reversed like that. But in any case, we can figure out what the change in the potential energy is by using the equation. ΔU=q⋅ΔV. So in this case now, we have a positive one electron charge because if this is a proton, then the charge on this guy is equal to plus e, and now the potential difference is negative one volt. So that means that the change in potential energy is negative one eV, just as it was for the protons. We get the same exact thing, and the fact that it's negative means that it is basically accelerating as it's going, and all the energy is being converted to kinetic energy.

So I have this little, this little variable here, or these little units, 1 eV, and that's actually has a precise definition. This one eV is actually called an electron volt. It's basically the change in the potential energy of 1 electron or really one proton as it travels through a one volt of potential difference. And basically, all this eV is, it is basically just a unit of energy for very, very small charges. So that's the whole entire thing. So basically, we're just going to use all of our energy formulas, but we're just going to have a different unit for it, and it's just going to be a conversion. Alright? So let's go ahead and check out an example. So we're supposed to figure out what is the speed of an electron with 100 electron volts of kinetic energy. So we are looking for the speed and we're given kinetic energy. So that means we're gonna use the relationship that the kinetic energy is equal to one-half m, and this is gonna be an electron. So it's gonna be me times v final squared. So we're just gonna sort of, like, assume that this thing goes from rest and is now traveling at some speed. Alright? So we gotta move everything over to the other side. The one half goes over, and the mass of the electron goes over as well. So now we have 2×k/me=vfinal squared. So that means that vfinal= 2×thekineticenergy Now the kinetic energy I'm told is 150 volts, but that's not in the right units that I need. So 150 eVs is gonna be 150 times 1.6×10−19 joules. And that's gonna give me in joules because I need that in order to plug it into this formula here for the velocity. I need to have these things in the right units. So, when you work this out, 150 electron volts is actually equal to 2.4×10−17 in joules. So this is the number I wanna plug in for this formula. So I've got 2 times 2.4×10−17 . And now I just need to divide it by the mass of the electron, which by the way is gonna be given to you on a test. It's gonna be 9.11×10−31 . And then you just have to square root that. So what you should get is you should get 7.26×10sixthmeters/second , and that's it. So basically, all of our equations for energy are gonna be working the exact same. It's just that an electron volt is just a slightly different unit of energy. So basically, we're just doing unit conversion here. Alright, guys. Let me know if you have any questions.

Here’s what students ask on this topic:

What is an electron volt (eV) and how is it defined?

An electron volt (eV) is a unit of energy commonly used in the field of atomic and particle physics. It is defined as the amount of kinetic energy gained or lost by an electron when it moves through an electric potential difference of 1 volt. Mathematically, it is given by the equation:

$\mathrm{\Delta U}=q\times \mathrm{\Delta V}$

where $\mathrm{\Delta U}$ is the change in potential energy, $q$ is the charge of the electron (approximately $1.6\times {10}^{-19}$ coulombs), and $\mathrm{\Delta V}$ is the potential difference (1 volt). Therefore, 1 eV is equivalent to $1.6\times {10}^{-19}$ joules.

How do you convert electron volts (eV) to joules (J)?

To convert electron volts (eV) to joules (J), you use the conversion factor that 1 eV is equal to $1.6\times {10}^{-19}$ joules. The formula for the conversion is:

$E\left(J\right)=E\left(\mathrm{eV}\right)\times 1.6\times {10}^{-19}$

For example, if you have 100 eV, the energy in joules would be:

$100\times 1.6\times {10}^{-19}=1.6\times {10}^{-17}$ joules.

What is the relationship between kinetic energy and electron volts?

The relationship between kinetic energy (KE) and electron volts (eV) is that kinetic energy can be expressed in electron volts when dealing with subatomic particles like electrons. The kinetic energy of a particle is given by the formula:

$\mathrm{KE}=\frac{1}{2}\mathrm{mv}{2}^{}$

where $m$ is the mass of the particle and $v$ is its velocity. When the kinetic energy is given in eV, it can be converted to joules using the conversion factor:

$\mathrm{KE}\left(J\right)=\mathrm{KE}\left(\mathrm{eV}\right)\times 1.6\times {10}^{-19}$

This allows for the calculation of velocity or other parameters using standard physics equations.

How do you calculate the speed of an electron given its kinetic energy in electron volts?

To calculate the speed of an electron given its kinetic energy in electron volts (eV), you first need to convert the kinetic energy to joules (J). Use the conversion factor:

$\mathrm{KE}\left(J\right)=\mathrm{KE}\left(\mathrm{eV}\right)\times 1.6\times {10}^{-19}$

Then, use the kinetic energy formula:

$\mathrm{KE}=\frac{1}{2}\mathrm{mv}{2}^{}$

Rearrange to solve for velocity $v$:

$v=\sqrt{\frac{2\times \mathrm{KE}}{m}}$

For example, if the kinetic energy is 100 eV, convert it to joules:

$100\times 1.6\times {10}^{-19}=1.6\times {10}^{-17}$ J

Then, use the mass of the electron $9.11\times {10}^{-31}$ kg to find the speed:

$v=\sqrt{\frac{2\times 1.6\times {10}^{-17}}{9.11}}=5.93\times {10}^6$ m/s

Why is the electron volt (eV) a useful unit in particle physics?

The electron volt (eV) is a useful unit in particle physics because it provides a convenient way to express the extremely small amounts of energy associated with subatomic particles. Since 1 eV is equivalent to $1.6\times {10}^{-19}$ joules, it simplifies calculations and comparisons in the context of atomic and particle interactions. Using eV allows physicists to avoid dealing with cumbersome scientific notation and makes it easier to communicate and understand energy levels, binding energies, and reaction thresholds in experiments and theoretical models. Additionally, eV is directly related to the potential difference experienced by charged particles, making it particularly relevant for describing phenomena in electric fields.