Question

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/cm". What would be the radius of a sphere of this material that has a critical mass?

Answer 1

Answer:

Radius = 9.0216 cm

Explanation:

Given that:

The critical mass of neptunium-237 = 60 kg

Also, 1 kg = 1000 g

So mass = 60000 g

Density = 19.5 g/cm³

Volume = ?

So, volume:  

$Volume=\frac {{Mass}}{Density}$  

$Volume=\frac {60000\ g}{19.5\ g/cm^3}$  

The volume of the material = 3076.92308 cm³

The expression for the volume of the sphere is:

$V=\frac {4}{3}\times \pi\times {(radius)}^3$

$3076.92308=\frac{4}{3}\times \frac{22}{7}\times {(radius)}^3$

$\frac{4}{3}\times \frac{22}{7}\times {(radius)}^3=3076.92308$

$88\times {(radius)}^3=64615.38468$

${(radius)}=\sqrt[3]{\frac{64615.38468}{88}}$

Radius = 9.0216 cm