The One Man (17 page)

For a moment, Alfred was certain the boy had already tired of him, and would just take his cap and walk out. Go back to the game that was clearly more fun, and had gotten him cakes and chocolates and all the adulation.

But to Alfred's surprise, he remained, his eyes shifting from bored and then reproved, to apologetic, and finally even to interested, filled with some contrition at the same time. “I'm sorry, Professor. I didn't mean to be rude. Please continue.”

Inside, Alfred smiled. Strip away the brashness, forgivable in such a precocious lad, and inside that perfect brain was an inexhaustible basin ready and waiting and an unquenchable curiosity to fill it with whatever knowledge there was.

“Good. Now to your question, boy, effusion is the rate of transference of a gas through a probe or, better yet, a membrane. Graham's Law postulates that if the molecular weight of one gas is two times that of another, it will diffuse through a porous layer, or even an opening the size of a pinhole, at the rate of the other times the square of two. It is the key postulate in the separation of isotopes—which have the same molecular structure yet different atomic weights.”

“Separating isotopes … Porous layers … Why do you need to teach me all this?” Leo shrugged, clearly already a bit bored.

“For now, just let this all soak into your head, lad. Look—” Alfred took out a piece of chalk. He had a tin sheet, a scrap of metal left from the motor shed. “All that matters now is how it's expressed as a formula.” Alfred scratched out:

He asked, “Do you have it?”

Leo stared at it, repeating it to himself. “I think so.”

“Therefore the
inverse
of this equation is…” Alfred erased it with his sleeve and wrote out a new formula, “that the
density
of a gas is directly proportional to its molecular mass.”

“Are you with me, son?” Alfred saw the boy's eyes glaze.

Leo nodded, a little fuzzily. “I guess.”

“All right, then give it back to me, please. Just as I have written.”

Leo shrugged. “The rate at which a gas diffuses is inversely proportional to the square root of its densities.”

“Good. Now, here, write it out as a formula.” Alfred handed him the chalk and tin and covered up what he had done. “Exactly as I gave it to you.”

Leo hesitated for a moment, blew out his cheeks, then wrote it,

just as Alfred had conveyed.

“Excellent. Now how about the inverse of that? For density?”

Leo thought on it a second. “The
density
of a gas is inversely proportional to its molecular mass.”

“No. Not inversely. The opposite of that. It's
directly
proportional,” Alfred corrected him.

“Excuse me, Professor…?” Leo scrunched his eyes.

“The density of a gas is
directly
proportional to its mass. It's the exact inverse of the first equation I gave you. You see—”

“All right. Sorry. I think I've got it now.” Leo wrote out the formula,

this time correctly. “
Directly
proportional. Then this would be the symbol—he drew it with a stylish flourish:

∝

“Very good. Now, in gaseous diffusion, we're dealing with the identical principle, except we are working with two radioactive isotopes. Uranium-235, which is a fissile property.
Fissile
meaning it can be split and is capable of creating what we refer to as a ‘chain reaction,' if separated from its more plentiful, but
not
fissile, cousin, U-238.”

“
Two thirty-five? Two thirty-eight?
Sorry, but my head is starting to feel like it's fissile, Professor.”

“Don't try and understand it all now. You know of uranium, right?”

“Yes. Its symbol is U. And I think it has the highest molecular weight of any element.”

“Second highest. But no matter, plutonium is only newly isolated and probably wasn't even on the element chart when you would have studied this. Uranium-235 occurs in a 0.139-to-one ratio in natural uranium ore. Meaning that only 7 percent of all uranium is U-235. The rest is 238. It's quite rare. The trick, then, is to separate this rare, highly charged isotope, which has the same properties but a different molecular weight than its more common relative, U-238. To do that, or at least to do that in the kinds of quantities you would be seeking, you need not only a diffusing membrane but the only compound of uranium sufficiently volatile to engender this, uranium hexafluoride, UF-6, which is completely solid at room temperature but sublimes once it approaches—”

“Sublimes?”
Leo's eyes started to glaze over again. “I'm afraid you're beginning to lose me, Professor.”

“Here…”
Alfred took the tin again and scribbled a far more complex equation. “Just memorize this…”

“Which is equal to, I think…” Alfred closed his eyes and went through a series of calculations in his head. “One point oh oh four two nine eight or something … Where—and this is important, Leo—RATE One is the rate of effusion of U-235 and RATE Two is the effusion of…?” He looked to Leo to finish.

“U-238,” Leo replied, after a moment of thought.

“Correct! And M
1
is the molecular mass of U-235 and M
2
the molecular mass of U-238. The slight difference in weights explains the 0.4 percent difference in the average velocities of their neutrons.” He looked at his student. “So how does that sit?”

“To be honest, it sits a bit fuzzily, Professor.”

“Keep at it. I know this might as well all be Greek to you right now…”

“No, Greek I actually studied in school…” Leo rolled his eyes.

“Look, you don't have to understand it all now. But what's important is that you have a basic grasp and commit the equations…” he drew a double line beneath the equation, “into that stellar brain of yours. So, look at it again. Let it sink in.”

Leo ran his eyes over the equation again, then closed them.

“Do you have it?”

“RATE small 1 over RATE small 2 is equal to the square root of M small 1 over M small 2 … Must I read you back all the numbers, Professor? I'm pretty sure I can … One point, zero, zero, four…”

“That's not necessary. Anyone with a third-level math degree can calculate that out.”

“Then, where Rsmall
1
is the rate of effusion of … UF6-235, and Rsmall
2
is the effusion for UF6-238, and M
1
…” Leo pressed a finger to his forehead, “the molecular mass of U-235, and Msmall
2
, the mass for 238. And so on, and so on, and so on…”

“Bravo!”
Alfred said, leaning forward and squeezing the boy's knee. He coughed up a bit of phlegm.

“One question, Professor, if you don't mind…?”

“Of course. Go ahead.”

“I still don't understand why you need to separate this U-235 from 238? And you said before ‘in sufficient quantities…' Sufficient quantities for what?”

“Let's not get ahead of ourselves.” Alfred cast him a patient smile. “All that is to come, my boy. To come.”

“So that's it? That's what you needed me to memorize? The physics that will save humanity?”

“That's Lesson One,” Alfred replied. “It's enough for today.”

“Lesson One…” Leo cocked his head a little warily. “
One
of…
?
”

“
Hundreds,
my boy.” Alfred slapped him on the shoulder. “Hundreds. However, I must warn you, tomorrow it actually starts to get a little complicated.”

 

TWENTY-THREE

Weeks went by. They met whenever they were able, for a few minutes at a time after roll calls in the mornings, before meals, most every day.

Other than Tuesdays, when Leo was usually summoned to play chess with the Lagerkommandant Ackermann's wife.

Which bristled Alfred. “Why do you choose to play a game when we have serious work to get done?”

“Because that
game,
as you call it, may one day be the difference in saving my life. And yours too, I should remind you. I tell her all the time that I share the treats she gives me with my uncle, the Professor. She promises to watch out for us.”

“Watch out for us … I think you just like to go because you are sixteen and you can stare at a woman's tits. I may be old, but not so old that I can't remember the pleasure in that.”

“That as well, I suppose.” Leo blushed, with just a little shame. “Still, she is nice to me. And, I believe, she is not her husband when it comes to what goes on in here. I think she is genuinely reviled by what she sees him do. That's why she helps with the sick at the infirmary.”

“You think that's so, huh? She shares all this with you?”

“She does. While we play.”

“I think that playing this game with you is how she puts her guilty conscience to rest,” Alfred said. “In a way, you are her absolution.”