The day Fermi switched on the first reactor
It's below freezing outside. Under the west stands of the University of Chicago's football stadium, 49 people are crowded into an old squash court around a pile of black bricks. You're one of them.
The thing in front of you is called Chicago Pile-1, and "pile" is exactly right. It's a squashed ball of graphite bricks about 7.5 metres wide, with lumps of uranium tucked inside. Wooden rods coated in cadmium slide through it. Cadmium soaks up neutrons like a sponge, so with the rods in, the pile sleeps.
Up on a platform, three young physicists hold buckets of cadmium solution, ready to drown the pile if something goes wrong. One man stands by with an axe, next to a rope that holds up an emergency rod. Everyone else is watching the neutron counters. The man in charge, Enrico Fermi, has a slide rule in his hand.
Before anything happens, make your calls.
Your predictions lock now. At the end of the day you'll see them next to what really happened.
Everything depends on one number.
A neutron hits a uranium nucleus and the nucleus splits, throwing out two or three new neutrons. Some escape the pile. Some are eaten by cadmium or by impurities in the graphite. The rest split more uranium.
On average, how many new neutrons does each neutron lead to? Fermi called that number . Grow a family of neutrons and watch what does.
Below 1, every family dies out. Above 1, it grows without limit. Exactly 1 holds steady, and that line is called critical. After generations:
Fermi's pile reached about k = 1.0006. Start with 1,000 neutrons. About how many are there after 1,000 generations?
Why it had to be so big.
This is a toy pile. Yellow dots are uranium lumps sitting in graphite. Tap inside it to fire neutrons in. A neutron that reaches the edge escapes. One that touches a yellow cadmium rod is eaten.
Make the pile bigger and a neutron has to travel further to escape, so it gets more chances to hit uranium first. That's why Fermi's team kept adding layers until the counters told them to stop.
The toy is simplified, but the idea is exactly right. Size controls how many neutrons escape, and the rods control how many get eaten. Together they set .
Pull it out six inches at a time.
After lunch, every rod is out except one. Fermi has it pulled out step by step. After each step the counters climb and then level off, and he checks the level against his slide rule. A pile below critical always levels off. A pile above critical never does.
Now you're in charge. Time here runs 20 times faster than real life.
Fermi's slide rule, one step at a time.
You've seen that the count grows. Fermi needed to know how fast, in minutes, because the people in the room had to be able to react. Here's how he got there.
Each generation multiplies the count by . After generations:
One generation lasts a time , so after seconds there have been generations. When is very close to 1, the power has a clean approximation:
Suppose you push the rod in a little, so is cut in half. What happens to the time it takes the count to double?
Set and solve for . Take the natural log of both sides:
sits on the bottom, so halving it doubles . That's exactly how the rod gave Fermi control: tiny changes in , big changes in how fast things moved.
Most neutrons from a split fly out almost instantly, within about a ten-thousandth of a second. But about 0.65% come out seconds later, released by the broken fragments as they decay. Those late neutrons stretch the average generation to about s.
Your turn: the calculation that decided the day.
Around 3:25 p.m., Fermi closes his slide rule and announces that the reaction is self-sustaining. The pens on the chart recorder keep climbing. You have the same numbers he did: and s.
How did your predictions do?
What happened next
You used the same three tools they did: exponential growth, a logarithm to undo it, and one tiny number, , that decides everything.