00:01
So we know that for part a, the formula for density would be the mass over the volume.
00:04
And we know that here, the average density of an atom is equaling 10 to the third kilograms per cubic meter.
00:15
The average volume of an atom, we're going to model the atom as a perfect sphere would be four thirds pi times the radius of an atom cubed.
00:25
And so the density of an atom would be equal to the mass of an atom divided by the volume of an atom.
00:33
And so we can then solve and say here that 10 to the third kilograms per cubic meter would be equalling the mass of an atom divided by four thirds pi times the radius of an atom cubed.
00:53
And so we can say that then the mass of the nucleus is almost the mass of an atom.
01:02
Atom.
01:03
So the mass of an atom is approximately equal to the mass of the nucleus.
01:08
And the nucleus of an atom has a radius about 10 fifth that of an atom.
01:15
So we can say that the radius of a nucleus is equaling 10 to the negative fifth times the radius of an atom.
01:22
And so the volume of a nucleus would be equaling to four -thirds pi times the radius of a nucleus cubed.
01:33
We then know that the density of a nucleus would be equaling the mass of the nucleus divided by the volume of a nucleus.
01:44
This would be equal to the mass of the atom, because the mass of the atom is approximately equal to the mass of the nucleus, divided by four -thirds pi times the radius of a nucleus cubed.
01:57
We are going to then substitute and say that the density of the nucleus is equaling the mass of an atom divided by four -thirds pi multiplied by 10 to the negative fifth times the radius of an atom, quantity cubed.
02:21
And this is equaling mass of an atom divided by four -thirds pi times the radius of an atom times 10 to the negative 15th power.
02:43
And so we can then, from this equation, we can substitute in and radius cubed...