Properties of the nucleus: If a nucleus had a diameter of 8.0 fm, what would be its expected mass, in atomic mass units?

Question

Quizplus · Accepted Answer

The mass of a nucleus can be estimated using its diameter and the fact that the nuclear density is approximately constant. The formula relating the mass number (A) to the radius (R) of a nucleus is $R = R_0 A^{1/3}$, where $R_0$ is a constant approximately equal to 1.2 fm. Rearranging this formula to solve for A gives $A = \left(\frac{R}{R_0}\right)^3$. Substituting $R = 8.0$ fm and $R_0 = 1.2$ fm gives $A = \left(\frac{8.0}{1.2}\right)^3 \approx 296$, which means the expected mass is about 296 atomic mass units (u).

Properties of the Nucleus: If a Nucleus Had a Diameter