### 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.