(a) Show that if you assume the average nucleus is spherical with a radius r = r₀ A^1/3, and with a mass of A u, then its density is independent of A.

(b) Calculate that density in u/fm³ and kg/m³, and compare your results with those found in Example 31.1 for ⁵⁶Fe.

Data from Example 31.1

(a) Find the radius of an iron-56 nucleus.

(b) Find its approximate density in kg/m³, approximating the mass of ⁵⁶Fe to be 56 u.

Strategy and Concept

(a) Finding the radius of ⁵⁶Fe is a straightforward application of r = r₀ A^1/3, given A = 56.

(b) To find the approximate density, we assume the nucleus is spherical (this one actually is), calculate its volume using the radius found in part (a), and then find its density from p= m/V. Finally, we will need to convert density from units of u/fm³ to kg/m³.