Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.

Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to calculate the density of a proton assuming it has a diameter of 1.2 femtometers. So density is mass divided by volume and we'll take the proton to be a sphere in which case the volume is four-thirds π times radius cubed and then multiply top and bottom by 3; these 3's cancel leaving us a 3 on top. So we have 3m over 4π times radius cubed but we'll write radius as diameter divided by 2 since we are given diameter and we'll cube that and in which case, we have a denominator of 8 because 2 cubed is 8 and 4 with that 8 in the denominator there makes a denominator of 2 underneath d cubed and multiply top and bottom by 2, we end up with 6m over π d cubed. So the density then is 6 times the mass of a proton divided by π times the diameter of a proton cubed which is 1.8 times 10 to the 18 kilograms per cubic meter.