Video Transcript
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.
