Neptunium. In the fall of 2002, scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a nuclear chain reaction. Neptunium-237 has a density of 19.5 g/cm3. What would be the radius of a sphere of this material that has a critical mass?

Solution 11E Critical mass of Neptunium-237 = 60 kg Density of Neptunium-237 = 19.5 gm/cm 3 3 Density = 19.5 × 1000 kg/m 3 Density = 19,500 kg/m If r is the radius, then the volume of a sphere is = 4r /3 We know that, V olume × Density = Mass 3 4r /3 × 19,500 = 60 3 3 r = 60 × 3/(4 × 19,500) m r = 180/(4 × 3.14 × 19,500) m 3 r = 0.000734 m 3 r = (0.000734) 1/3m r = 0.09 m r = 0.09 m × 100 r = 9 cm Therefore, the approximate radius of the Neptunium-237 sphere is 9 cm.