HS #64 2020.11.12
Boron Rods
I remember it vividly. My 6th grade science class was watching a film that explained nuclear reactions – a reaction caused when a neutron smashes into a uranium-235 nucleus releasing three more neutrons and a bit of energy. The resulting exponential growth in the number of neutrons results in a nuclear explosion.
To demonstrate it, the floor of an entire room was covered with mousetraps – each with a ping pong ball perched on it. When a single ball was tossed into the room, it sprang a trap releasing another ball, and those two landed on two more traps which released their balls. Almost instantly the air was filled with flying ping pong balls. This is what destroyed Hiroshima and Nagasaki.
In order to explain exponential growth to my math classes, I use the great-grandpa example. Suppose you have two ancestors who 200 years ago each deposited $10 in a bank at 6% annual interest. The first included directions that each year the interest be removed and collected in a jar, while the other directed that the interest stay in the bank to earn additional interest.
The first account grows at a constant rate of 60 cents each year, so after five years there is $13.00 and after 200 years a total of $130. What about the second? At the end of the first year, you have $10 times 1.06 = $10.60. A 60¢ increase. Second year: $10.60 times 1.06 = $11.24. A 64¢ increase. Then a 67¢ increase. Then 71¢. After five years, you have $13.38 – 38¢ more than the first. How much after 200 years? A whopping $1,151,259.04
Unlike linear growth which increases at a constant rate, exponential growth happens whenever the amount of change is not constant but instead grows proportional to the amount present. Whether a bank account, a nuclear bomb, zebra mussels, or small pox which decimated continents, the result is the same: unconstrained explosive growth.
So how then do we harness nuclear energy to safely produce electricity? Boron rods are positioned in the reactor chamber to absorb enough of the particles to keep the chain reaction from going wild. If pushed in all the way, the reaction stops. If pulled out, the reaction turns into an explosion. Simple.
When the Manhatten Project under the bleachers at the University of Chicago tested the first nuclear reaction, Enrico Fermi and company had done all the calculations on slide rules to assure that things would go as planned. But so great was the consequence of a miscalculation that a physicist stood ready with an ax to drop control rods into the reactor if needed. They also considered positioning a suicide squad of three young physicists on the ceiling with containers of cadmium-sulfate (neutron-absorbing) solution.
By absorbing just enough of the neutrons, they achieved an exponential rate of 1.0006 (equivalent to a tiny interest rate of 0.06%), but that was enough to convince them that the theory of Einstein and Bohr really worked. Had they not put the control rods back in place, within 90 minutes the one-half watt of power would have multiplied to a million kilowatts – vaporizing them and melting the room.
What do the boron rods do? By absorbing neutrons, they lower the exponential rate to a number less than 1. In the same way that 1.0006 multiplied by itself enough times will increase without bound, so also a number less than 1, say 0.9995 multiplied by itself repeatedly will head to zero. Lower the average number of released neutrons to less than 1, and the reaction dies down – similar to a bouncing ball coming to rest.
Do you see where this is going? Our present coronavirus is a biological explosion. Social distancing and masks for all of us and isolation for those who test positive are our only effective “boron rods.” Without them, the virus will explode through the human population. If we wear them and responsibly distance and isolate ourselves, the multiplier rate will be less than 1, and the number of people with the virus will head to 0 – as it has done in China.
Unfortunately, as with out-of-tune singers in a choir, even though most are responsible, a few people can have a big negative effect, thus raising the multiplier above 1. If 99% of cars are low-exhaust, but 1% are heavy polluters, the air is bad. The key is for EVERYONE to be responsible. Nothing else will do it. The math is simple.
