# Lesson Video: The Electron Volt Physics • 9th Grade

In this lesson, we will learn how to define the unit of an electron volt and how to convert between electron volts and other energy units.

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### Video Transcript

In this video, our topic is the electron volt. The electron volt is a unit of energy. And in this lesson, we’ll learn why it’s useful, how to define it, and how to use it practically.

First off, let’s consider why this unit exists in the first place. We know that there’s already an SI base unit of energy. That’s the joule. The way we define a joule is that it’s the energy needed to apply a force of one newton over a displacement of one meter. Based on this definition, we could say that a joule is well-suited to describe everyday-life-type processes, for example, lifting a box up onto a shelf or driving a car down the street and so on. We know, though, that there are many physical phenomena that occur at a much smaller scale than this, anything, say, on an atomic scale having to do with individual atoms or molecules or if we think of individual packets of light, photons. Processes like these can involve energies on a much smaller scale than the framework that we use to define a joule.

A primary motive then for having a unit of energy called an electron volt is so that we can conveniently describe energies related to these smaller scale processes. Now we said that the definition of a joule is the energy needed to apply a force of one newton over a displacement of one meter. The way we define an electron volt is like this. Say that we have one conducting plate here and another right over here. And say further that we set up a potential difference of exactly one volt between these two plates. If we put a single electron on one of these plates, and then we have it move from that plate to the other, then the energy it takes to do that is equal to one electron volt. So we now see where this name electron volt comes from. It’s because we’re working with a single electron moving across a potential difference of one volt.

The way we abbreviate this unit is like this: lowercase e capital V. And as we said, one electron volt equals the energy involved in moving one electron across a potential difference of one volt. Now, if we compare an electron volt to a joule, we can see just based on their definitions how different these two amounts of energy will be. We might guess that a joule is much larger than an electron volt. And that’s correct. In fact, one joule of energy, to three decimal places, is equal to 6.242 times 10 to the 18th electron volts. This means we would need roughly 1 billion billion electron volts to have one joule of energy. Or we could write this the opposite way that one electron volt is roughly equal to 1.602 times 10 to the negative 19th joules. The point is though both joules and electron volts are units of energy, an electron volt is much smaller than a joule.

Keeping these conversions in mind and clearing the rest of our screen, we can think of a few physical situations where it will be useful to talk of energy in terms of electron volt units rather than in terms of joules. For example, when we’re considering photons of visible light — here’s a red one, a yellow one, and a blue one — in units of electron volts the energy of each of these photons is two to four electron volts. Or if we think on an atomic scale, say that we have two atoms of silicon bound together by a covalent bond — meaning that they share two electrons — the energy needed to break this bond is on the order of one electron volt.

In smaller scale situations like these then, stating our energies in units of electron volts is typically more convenient than using joules. We could write these energies in joules, but that would make them a bit more difficult to understand at first glance and also a bit more difficult to compare visually. So we do sometimes find an advantage in using this electron volt unit for energy.

Now it’s not uncommon in an example exercise or some other kind of question to want to convert between these two energy units, electron volts and joules. To do that, we’ll want to keep these conversions in mind, but there’s another aspect to consider as well. And that is that often times units are preceded by what are called unit prefixes. Some examples of prefixes include kilo-, abbreviated k, indicating a multiple of 10 to the third of whatever unit is involved; mega-, indicated by capital M, which signifies multiplying by 10 to the sixth or one million; giga-, capital G, representing multiplying by 10 to the ninth or one billion; tera-, capital T, representing 10 to the 12th or one trillion of some unit and so on. The prefixes can continue getting larger and larger.

Now we bring all this up because understanding these prefixes and keeping them in mind when we convert one energy unit to another can be very important. For example, if we wanted to convert, say, 7.3 giga-electron volts into joules, then we would need to know what this giga- prefix means. And we would include that in our understanding of converting from electron volts, specifically giga-electron volts into joules. The best way to understand how this all fits together is to work through some example exercises. So let’s look at one of those now.

What is eight times 10 to the negative 19th joules in electron volts?

Okay, so here we have an amount of energy quoted in the specific unit of joules, and we want to state what that amount of energy is equivalent to in a different energy unit, electron volts. So we have some set amount of energy, and we’re changing the way we represent it from joules to electron volts. To figure out how to make this conversion, let’s recall how many joules are in one electron volt. If we write out this conversion to three decimal places, then we can recall that one electron volt is equal to 1.602 times 10 to the negative 19th joules. We want to apply this ratio to this number right here to remove the unit of joules and replace it with electron volts. To do that, we can multiply our energy in joules by this ratio.

Notice two things about it. First, the value we have in our numerator is equal to the value in our denominator. That’s true based on this equation over here. So effectively, by multiplying by this fraction, we’re just multiplying our energy in joules by one. But what this multiplication will do, and this is the second thing we can notice, is cancel out the unit of joules in our energy value and replace it with the unit of electron volts. We see that this takes place because we have a unit of joule in our numerator and in our denominator. And therefore, those units cancel. So that when we carry out this multiplication, we’ll be left with a value in units of electron volts.

Entering the expression on our calculator, we find a result to one significant figure of five electron volts. Now, we keep just one significant figure because we only had one in our original energy value. We can say then that eight times 10 to the negative 19th joules is equal to five electron volts.

Let’s look now at a second example exercise.

What is 14 electron volts in joules? Give your answer to three significant figures.

In this example, we have an amount of energy in units of electron volts. And we want to convert it into a different unit, the unit of joules. Both electron volts and joules are units of energy. So to figure out how to make this conversion, we’ll want to recall how many joules are in one electron volt. To three decimal places, one electron volt is equal to 1.602 times 10 to the negative 19th joules. So then we have our conversion factor from one unit to the other. And we’ll want to multiply this given amount of energy by that factor so that we end up with the same overall energy amount but expressed in joules rather than electron volts. To do this, we want to multiply this given energy amount by some fraction which will cancel out the units of electron volts and leave us with units of joules.

To figure out what that fraction will be, we can look over here at our unit conversion equation. If we want the units of electron volts to cancel out — and we do — then in the denominator of our fraction, we’ll want to put an energy amount in those units. And then up top, we’ll want to put in an energy value in units of joules where that total energy is the same as one electron volt. Well, we’ve seen that one electron volt equals 1.602 times 10 to the negative 19 joules. So that’s what we’ll put in our numerator.

Notice then that this fraction, by which we’re multiplying 14 electron volts, is equal to one. And we can also see that when we carry out this multiplication, the units of electron volts will cancel out. And we’ll be left with an energy in units of joules. When we calculate this product to three significant figures, we find a result of 2.24 times 10 to the negative 18th joules. This is how many joules of energy 14 electron volts is equal to.

Let’s now look at one last example exercise.

What is 30 kiloelectron volts in joules?

In this exercise then, we’re converting an amount of energy from one unit, kiloelectron volts, into another, joules. To get started doing this, we can recall just how many joules of energy are in one electron volt. A single electron volt is equal, to three decimal places, to 1.602 times 10 to the negative 19th joules. In our given energy value though, we see that we’re not only working with electron volts but rather kiloelectron volts. This letter k is what’s called a unit prefix. And we can recall that it represents a kilo of whatever unit is involved, which means 10 to the third or 1000 times that unit. So then a kiloelectron volt is 1000 volts.

Knowing this, we can rewrite our energy value in units simply of electron volts. It’s 30 times 10 to the third eV. In doing this, we’ve accounted for our unit prefix kilo-. And now we have a straight line of sight into converting our energy from electron volts into joules. The way we’ll do this is we’ll multiply our energy by a fraction. The denominator of that fraction will be one electron volt. We do this so that when we multiply through, the units of electron volts cancel out. And the value we’ll use in our numerator is 1.602 times 10 to the negative 19th joules. Note that this is equal to one electron volt.

When we carry out this multiplication, we’ll get a result in units of joules. And in doing this, if we keep two significant figures in our final answer because we were given an energy originally with two significant figures, then we find a result of 4.8 times 10 to the negative 15th joules. That’s 30 kiloelectron volts in joules.

Let’s summarize now what we’ve learned about the electron volt. In this lesson, we saw that the electron volt, abbreviated e capital V, is a unit of energy. Specifically, it’s the amount of energy involved in a single electron moving across a potential difference of one volt. Electron volt energies may involve unit prefixes, such as kilo-, mega-, giga-, and tera-. And lastly, we saw that energies can be converted from units of joules to electron volts or electron volts to joules. One electron volt, to three decimal places, is 1.602 times 10 to the negative 19th joules, while one joule, again to three decimal places, is 6.242 times 10 to the 18th electron volts.