## Building a nuclear bomb

### How to get 'critical'

It's harder than you think to start a chain reaction:

• Higher purity -> technically difficult, but removing U-238 means less (fast) neutron absorption.
• If you had two chunks of the same weight of pure U-235, which shape would be more likely to start a chain reaction?

In which shape would an emitted neutron be more likely to run into another U-235 nucleus?

### Critical mass

The critical mass is the minimum amount needed to keep a chain reaction going.

Pure U-235 - 50 kg sphere

Pure Pu-239 - 10 kg

### A-bomb

style="text-align: right"> Bring 2 pieces that are not critical together into one that *is* critical.

But where will the neutrons needed to *start* the chain reaction come from???

For 10 kg of Uranium-235, there is on average 0.1 neutrons / sec from spontaneous fissions, or one spontaneous fission each 10 sec.

It takes about 0.001 s ($10^{-3}$ seconds) for the two chunks to slide into place.

#### Plutonium

"Weapons-grade" plutonium-239 still has about 5% plutonium-240, with a spontaneous fission rate (0.05 kg out of 10kg) of 46,000 neutrons / sec from spontaneous fissions, or 1 fission each $2.2\times 10^{-5}$ sec.

What will happen if it takes $1\times 10^{-3}$ sec to make the critical mass?

So, you can't build a plutonium bomb the same way: the plutonium would fizz as the chunks get close, but not explode.

To make a plutonium bomb, you have to assemble the critical mass much faster: within a micro-second ($10^{-6}$ seconds).

This is done by packing explosives around a sub-critical mass of Pu, and setting them off to compress (implode) the plutonium.

### The Manhattan project

1939 - Einstein lends his name to a letter, written by Szilard, warning Roosevelt of the potential for a new kind of weapon based on chain-reaction fission in Uranium.

1941 - Japan attacks Pearl Harbor.

1942 - The Manhattan Engineering District turns earnestly into a bomb-making project. Two tracks will be pursued:

1. a ${}^{235}$U bomb, and
2. a Plutonium bomb.

### ${}^{235}$U bomb

One ${}^{235}U$ nucleus is chemically identical to the 140 ${}^{238}$U that surround it. How to separate out the fissionable ${}^{235}$U?

A huge gas diffusion plant was built at Oak Ridge, TN, that would eventually consume power at a greater rate than all of New York City, and deliver ~50 kg of ${}^{235}$U by the end of the war.

### Gas centrifuges

More recently the U.S., and countries like Pakistan have used gas centrifuges to enrich the Uranium.

Uranium is made into a gas -- $UF_6$-- and spun rapidly in such a cylinder. The heaver isotopes settle towards the outside of the container.

### How to... make Plutonium

When ${}^{238}$U is bombarded with neutrons in a nuclear reactor, it does not fission and give off more neutrons, but instead...

### Plutonium bomb

Plutonium: also more than 1 excess neutron per fission.

Can be chemically separated from U.

Technically more difficult to go critical.

A reactor at Hanford, WA was constructed to generate Plutonium.