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

Radius = 9.0216 cm

Step-by-step 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}* \pi* {(radius)}^3`

`3076.92308=(4)/(3)* (22)/(7)* {(radius)}^3`

`(4)/(3)* (22)/(7)* {(radius)}^3=3076.92308`

`88* {(radius)}^3=64615.38468`

`{(radius)}=\sqrt[3]{(64615.38468)/(88)}`

Radius = 9.0216 cm