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?

Video transcript

Hello everyone. So in this problem in the laboratory a certain liquid that is heavier than water was synthesized and it has a mass of 70 mg. This particular liquid has a density 10% higher than that of water. If this certain liquid would be frozen into a cube, what would be its side length? So you can start out by recalling what density formula is row which is density is equal to the mass oops mass divided by the Boeing and it is a liquid which is frozen into a cube. We know that the volume of a cube is simply the side length cube. So we can rewrite it as rho is equal to m over as cube. And now we can try to solve for s cube is equal to m overall. Now we want to find Row and were given the mass of 70 mg. And we're also told in the problem that this liquid Has a density 10% higher than that of water. You recall the row or density of H liquid Is equal to 1.0 g per cm cubed. And so that this particular liquid, let's say row X is equal to 1.1 times 1.0 g per centimeters cubed as it is 10% higher and that of water. So the row X. In this equation we're using Is 1.1 g 1st cm cute. We get finally that the equation for this side length, The mass, 70 mg over 1.1 g per centimeters cubed. And we notice that milligrams and grams won't cancel out. So we have to make a unit conversion Milligrams in one g. And we can simply just take to solve for the side length the cube root of this expression, 70 mg Over 1. g for cm cubed times the one g per 1000 milligrams. Let me get that. S. is approximately equal to 0.4 cm. Just answer choice. Hope themselves have a great day.