Question Video: Definition of a Second Physics

Which of the following SI units is defined as being equal to the interval in which atoms of cesium-133 emit 9,192,631,700 waves? [A] The meter [B] The mole [C] The candela [D] The second [E] The steradian

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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.

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