Verify that a 2.3 x 10¹⁷ kg mass of water at normal density would make a cube 60 km on a side, as claimed in Example 31.1. (This mass at nuclear density would make a cube 1.0 m on a side.)

Data from Example 31.1

Find the radius of an iron-56 nucleus.

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

Strategy and Concept

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

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.