### Video Transcript

In this video, our topic is SI unit
definitions. We’re going to learn what are the
seven basic SI units, called base units, and we’ll also learn how these basic units
are defined. We’ll come to see that even though
the definitions of these base units have changed over time, that doesn’t mean
they’re arbitrary. Rather than reflecting one person’s
perspective, the SI base unit definitions are carefully thought out and agreed upon
by a body of scientists that meets specifically to discuss these issues.

Now, when we talk about base units
— whether we’re specifically talking about the SI system, like we will in this
video, or some other system of units — pretty much any system includes base units
for these three quantities: length, mass, and time. And we can see the reason why. These quantities have so much
relevance to our daily life. When we consider these quantities
within the SI system, the base unit of length is the meter, abbreviated lowercase m;
the base unit of mass is the kilogram, abbreviated kg; and the SI base unit of time
is the second. Taken together, it’s possible to
describe many different physical quantities using these units.

For example, if we divide some
length in meters by some amount of time in seconds, then we’ve derived this quantity
we can call speed in units of meters per second. When we do a calculation like this,
we’re taking fundamental units. That’s another way of describing
base units, in this case meters and seconds. And we’re combining them so as to
create what’s called a derived unit, meters per second. Another example of this process is
to multiply a mass quantity expressed in the base unit of kilograms by a length,
written in meters, and then dividing that by a time, in seconds, squared. When we combine base units this
way, what we’re calculating is a force in units of newtons. In this example, the newton is the
derived unit, while the fundamental units involved are the kilogram, the meter, and
the second.

Now, even though we can get pretty
far in describing physical phenomena by combining these three units in various ways,
there are some things that they just don’t describe. One example of this is electric
current. There’s no way to combine meters
and kilograms and seconds to be able to describe an electric current. The same thing is true for
temperature values, also something we can call the amount of a substance. And along with this, scientists
have identified one other quantity, called luminous intensity, which essentially
refers to the brightness of a light source, that we would like to be able to
quantify using a unit but that we’re not able to describe using these three base
units.

So, in recognition of these four
additional quantities we would like to be able to measure, within the SI system,
four more base units were added. The ampere was added to describe
current. The kelvin was added to describe
temperature. And then the mole and the candela
were added to describe amount of a substance and luminous intensity,
respectively. So then, within the SI system as it
stands today, there are one, two, three, four, five, six, seven base units. And taken separately or combined
together, as we saw earlier in coming up with speeds and forces, we’re able to
describe most of the quantities of physical interest to us using these base
units.

Now, one of the most important
things about a base unit is how it’s defined. That is, what is one meter or what
is one kilogram or one ampere? It’s only when we knew these
definitions that we can connect real, measured quantities, of lengths or masses or
electric currents, with the units that we use in this system. So, let’s look now at just what the
definitions for these seven base units are. Now, interestingly, as we
mentioned, some of these definitions have changed over time. That’s because they continue to be
refined for maximum usefulness and clarity. The meter, for example, used to be
defined as the length of a particular rod made of a particular metal alloy
maintained at a temperature of zero degrees Celsius.

In this circumstance then, we had a
rod which was literally the meter. But to make this definition more
precise, it’s been changed so that now if we take an atom of krypton-86, a
particular isotope of the atomic element krypton, and let it oscillate in a vacuum,
emitting light that to our eyes would look red or orange, then knowing the
wavelength of that radiation, then if we take 1650763.73 of those wavelengths, then
we’ll have a total distance which is now the definition of a meter. In this definition, this number
here may seem arbitrary at first glance. But by defining a meter to this
level of precision, the accuracy of length measurements can be improved.

So, this is the definition for a
meter. And now let’s consider the
definition of a kilogram. In defining this unit, there is a
mass made of platinum and iridium, which is kept under vacuum at the International
Bureau of Weights and Measures in Paris. And the mass of this particular
object is considered to be the mass of a kilogram. So, if someone asks, what is the
mass of a kilogram? The answer is the mass of this
object right here. Now, let’s consider the definition
of the base unit of second. For a while, the second was defined
in terms of the divisions of a day. There are 24 hours in a day and
3600 seconds in an hour. And so, that gave a basis for
defining what fraction of a day a second represented.

But just like the meter, this
definition has been updated over time. The way to define a second now
involves taking an atom of cesium-133. And as this atom naturally
oscillates, it will emit electromagnetic radiation. Now, if we were to stand at a point
along this passing wave and count the amount of time it took for 9192631700
wavelengths to pass us, then that amount of time is defined as one second. So just like the meter, the second
is defined in terms of emissions from atoms.

Now, let’s consider the definition
of this unit, the ampere. Amperes are designed to quantify
electric current. And as such, we might expect the
definition to involve electric charge, and it does. In fact, the ampere is defined in
terms of the basic unit of charge, the charge of an electron.

If we take the charge of an
electron to be exactly 1.602176634 times 10 to the negative 19th coulombs, then we
can use this number along with the fact that a coulomb is equal to an ampere times a
second to define the unit of the ampere. Looking at this equation, we could
say that we’ve already defined the left side because that’s the charge of an
electron. And then, the SI base unit of
second is defined as we saw above. And that means, in this equation,
coulombs and seconds are precisely defined, which means that we can define the
ampere in terms of them.

Moving on to consider the
definition of the kelvin, we can recall that the coldest temperature possible,
what’s called absolute zero, is zero kelvin. But then, say that we had some
object at absolute zero. If its temperature increased, say
by one kelvin, how much of an increase would that correspond to? This is where the definition of
kelvin is needed. This definition is based on a
constant value in physics called the Boltzmann constant. This is a constant like the charge
of an electron or the Planck constant.

If we define this constant, often
symbolized using the letter lowercase k, to be exactly this value here, and we use
units of joules per kelvin to describe this constant, then in that case, we can
define the kelvin using the same approach we use to define the ampere. That is, we express the other units
in this expression, specifically the units of joules, which consist of kilograms and
meters and seconds, in terms of their already-defined values. So, if all the SI base units that
make up a joule are known precisely and the Boltzmann constant is known precisely
too, then those two things together give us a precise definition for kelvin.

Now, as we consider the basic
definition of a mole, it’s a bit more straightforward than the ones we’ve seen so
far. We simply state that one mole of a
substance is equal to 6.02214076 times 10 to the 23rd entities of that
substance. And this word “entities” might
refer to atoms or molecules, or it could even refer to something larger. Say an entity was a grain of
sugar. Well then, one mole of sugar grains
would be 6.02214076 times 10 to the 23rd grains of sugar.

And lastly, we come to the
definition of the unit for luminous intensity, the candela. This might be the least familiar of
the seven SI base units. But looking at this word “candela,”
we might guess what it refers to. This looks like the word for
candle. And indeed, one candela of luminous
intensity is about how much light a single candle gives off. Today, though, a candela is defined
more precisely. What we do is we say that radiation
at a certain particular frequency, 540 times 10 to the 12th hertz, is exactly equal
to this quantity here, 683 candelas times steradians divided by watts.

The watt is the SI unit of power,
which can be defined in terms of the base units of meters, kilograms, and seconds,
while the unit steradian refers to what’s called a solid angle so that if we had a
sphere like this one, if we were to pick out an area on the surface of the sphere
that’s equal to the radius of the sphere squared, then the distance from that
surface to the center of the sphere is also 𝑟. And that means that this whole
solid angle we’ve identified here is one steradian. So then, in this equation for
defining a candela, we precisely know our frequency. We precisely know watts and
steradians. And on that basis then, we can
define one candela of luminous intensity. So, those are our definitions of
the seven SI base units. Let’s look now at an example
exercise involving these units.

Which of the following SI units is
defined as being equal to the interval in which atoms of cesium-133 emit 9192631700
waves? (A) The meter, (B) the mole, (C)
the candela, (D) the second, (E) the steradian.

There are a couple of different
ways to answer this question. One way is to recall the
definitions for each of these five SI units. So then, we can recall that the
meter, for example, is defined in terms of a certain number of wavelengths given off
by the atomic isotope krypton-86. And likewise, we could recall
similarly precise definitions for the other SI units here. But a second way to answer this
question, one that doesn’t require knowledge of numbers with many significant
figures, is to think not in terms of the definitions of each of these terms, but
rather what physical quantity they measure.

Thinking along those lines and
starting at the top of our list, we can recall that the meter is the SI base unit
designed to measure length. That’s the physical quantity that
some amount of meters represents.

And then what about option (B) a
mole? This unit is used to indicate an
amount of a substance. So, for example, we could have one
mole of sodium chloride or one mole of water.

Moving on to the candela, this unit
may be less familiar to us. But the name of the unit itself can
give us a hint as to what it indicates. Candela sounds a bit like
candle. And indeed, this unit is used to
indicate the brightness or luminous intensity of some light source.

Moving on to option (D) the second,
we know that this unit is meant to measure quantities of time.

And then, lastly, the unit of a
steradian, in this word “steradian,” we see the word “radian.” And that can help point us to the
quantity that steradians indicate. A radian, we know, is an angle. One radian, by the way, is
indicated by an angle, where the arc length subtended by that angle is equal to the
radius of the circle that this angle is inscribed within. Now, when we go from a radian to a
steradian, we move from an angle in two dimensions like this to an angle in three
dimensions, what’s called a solid angle. So instead of a circle, we now have
a sphere.

And if we consider a
three-dimensional angle, starting from the center of the sphere, that covers an area
on the sphere’s surface equal to the radius of the sphere squared, then that tells
us that this three-dimensional or solid angle here is equal to one steradian. So anyway, this is the quantity
that steradians measure.

Now that we know all this, let’s go
back to our problem statement. This statement describes a unit
that’s being equal to an interval in which certain atoms of cesium-133 emit a
certain number of waves. Knowing this, we can tell that this
interval, whatever unit it corresponds to, is not, for example, an amount of a
substance. We can also tell that this interval
doesn’t refer to some amount of luminous intensity or brightness of some light
source. And as well, there’s no
directionality associated with this interval. It doesn’t occur over a certain
angle or over a certain direction. So we can say this interval does
not refer to a solid angle. All this means we can eliminate the
mole, the candela, and the steradian from consideration.

So then, is this interval we’re
talking about a length or is it a time? Well, notice that we’re told a
specific number of waves being emitted by these cesium-133 atoms. But we’re not told the wavelength
of these waves. And in general, depending on the
energy level of these atoms, that wavelength could be shorter or longer. And so, it seems that this
definition isn’t indicating a specific length. Rather, it seems to point to some
amount of time in which this number of waves can be emitted by these atoms.

Now, if we’re still unsure which of
these units to choose between, the meter and the second, we can be helped by
recalling what we can of the definitions of these units. Remember, we said that a meter is
defined in terms of a number of wavelengths emitted by krypton-86. That’s certainly different from
cesium-133. So, that would incline us to choose
the second as our answer. And then finally, if we are able to
recall the definition of a second, we’ll know that that definition matches up with
this description here. All this shows us that it’s not the
meter which is the SI unit being described here, but instead it’s the second. One second is the time interval in
which atoms of cesium-133 emit 9192631700 waves.

Let’s now summarize what we’ve
learned about SI unit definitions. In this lesson, we saw that within
the international system, or SI, there are seven base units. These are the meter to indicate
lengths, the kilogram that describes mass values, the second that indicates time,
the ampere that indicates electric current, the kelvin that tells what the
temperature of an object is, the mole which indicates the amount of a given
substance, and, lastly, the candela which tells us about the luminous intensity or
the brightness of a source of light.

We saw that these seven base units
are also called fundamental units and that by combining them it’s possible to create
what are called derived units. We saw, for example, that when we
divide a length by an amount of time, that gives us a quantity we often call
speed. And the units of speed, meters per
second, are considered a derived unit. And that’s because they’re made up
of the fundamental units of meters and seconds.

And lastly, in this lesson, we
studied the definitions of each one of these seven base units. We saw how, in some cases, the
definitions have remained the same over long periods of time, while in others,
they’ve been updated to increase accuracy and clarity. This is a summary of SI unit
definitions.