Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). Calculate the volume of the nucleus and the volume of the atom.

Video transcript

Hello everyone today. We are being given the following problem and asked to solve for it. Since the atom oxygen 16 has eight protons and eight neutrons. Its nucleus has a radius of around 3.0 to 50 m while atomic radius is about 48 kilometers. What is the volume of the nucleus and what is the volume of the atom? So first we have to assume Adam itself is a sphere so that we can use the volume of a sphere equation, which says that the volume of a sphere is able to 4/3 pi r cubed. We must then take note to convert our radius from centimeters to meters. And so in our questions still we have 3.02 50 m and we can use different conversion factors. In this case we're gonna use the conversion factor that 1 50 m is equal to to the negative 15th meters. And then we're gonna convert our meters into PICO meters. We can see that one pick a meter is equal to 10 to the negative m. Our units are going to cancel out and we're going to be left With 3.02 Times 10 to the negative 3rd m solving for our volume of our nucleus. We have 4/3 pi. And instead of r we're gonna replace that with the nucleus, the radius that we just sold for, which is 3.2 times 10 to the negative third meters giving us 1.2 times 10 to the negative seven m cubed. We can then find the volume of the atom by using the same equation four thirds pi r cubed. And instead of the radius of the nucleus, we're going to use the radius of the atom, the atom itself, which is 48 meters. We're gonna cube that and we're gonna end up with The answer of 4.6 times 10 to the 5th m cubed. And these are our final two answers the volume of the nucleus and the volume of the atom. I hope this helped, and until next time.