The diameter of the he nucleus is about 2.0 fm. assuming the nucleus to be a sphere, calculate its density in g/cm3.

Let us define first the unit of fm which means femtometer. It is equivalent to 10⁻¹⁵ of a meter. If you convert this to centimeter, the conversion would be 1 fm = 10⁻¹³ cm. Let's solve for the volume of the sphere of the nucleus:

V = 1/4*πd² = 1/4*π*[2 fm * (10⁻¹³ cm/1 fm) ]²

V = 3.1416*10⁻²⁶ cm³

The mass of the nucleus should be known to determine the density. According to literature, the mass of a Helium nucleus is 6.64 * 10⁻²⁴ g.

Density = 6.64 * 10⁻²⁴ g/3.1416*10⁻²⁶ cm³

Density = 211.36 g/cm³