Math

On Sunday, I watched the Washington Redskins, I mean, I watched the Washington Football Team (the new name may be politically correct but I'll never unlearn the name Redskins) play their longtime rival, the Dallas Cowboys.

Of course, watching football and listening to play-by-play doesn't provide sufficient mental stimulation so as I watched the game I also read the latest science news, and I was intrigued by one particular article.

German researchers just measured the time required for a photon to travel the diameter of a hydrogen molecule (chemical name: dihydrogen). A hydrogen molecule is tiny, and light travels fast, so the time interval for light to pass through a hydrogen molecule is a super-tiny number. The Germans said the time interval was 247 zeptoseconds. (A zeptosecond is 10^-21 s — a decimal point, 20 zeroes, and a 1.)

I thought, "I wonder if that's true. I'd better check their math."

(The Washington Football Team is outscoring the Cowboys big-time. In Britain they would say, "the Washington Football Team are outscoring the Cowboys" because the Brits consider a group to be a plural noun.) Either way, the Cowboys are taking some butt-kicking.

I don't know how big a hydrogen molecule is, but it's not spherical so the width depends on how you look at it. I decided to calculate the time it takes a photon to traverse a hydrogen atom (atom, not molecule) which is smaller than a molecule, and it's spherical so orientation doesn't matter.

The time required for a photon to travel across a hydrogen atom is the diameter of a hydrogen atom's electron shell divided by the speed of light:

1.06 x 10^-10 meters divided by 3 x 10⁸ meters per second

(While I was doing my back-of-the-envelope math, the game ended. The Redskins (you know who I mean) won 25 - 3. It was Washington's second win of the season, making them 2 - 5. Another game came on—the San Francisco 49ers at the New England Patriots. The Pats are six-time NFL champions. This game would be the first this season that I would see the Patriots play.)

After doing the math, I get 0.353 x 10^-18 seconds = 353 x 10^-21 seconds.

And that, folks, is 353 zeptoseconds!

But the math for the photon's transit time through a hydrogen atom is simple, so why is the answer 353 instead of 247?  And this is for a single hydrogen atom. A hydrogen molecule is larger and should therefore produce a larger number. There must be a problem, either with my diameter of a hydrogen atom or with the number for the speed of light. The speed of light has been measured many times to a high degree of accuracy. If we (meaning science) did not have the correct number for the speed of light, GPS systems wouldn't work. We can rest assured we know the speed of light very exactly. The number is 299,792,458 m/s, and I rounded it up very slightly to 300,000,000 m/s (3 x 10⁸ m/s). 

(The 49ers had an easy time defeating the Brady-less Patriots. The Pats are a 2 - 4 team so far this season. The Pats' new quarterback, Jarrett Stidham, has his work cut out for him. Somebody tell Coach Belichick that his team may not be going to the playoffs this year.)

But if the speed of light is correct, the problem must lie with the diameter of a hydrogen atom. It can't be 1.06 x 10^-10 meters. It must be a little bit smaller. To be precise, it must be 247/353 or 0.7 of our assumed diameter. I think the measurement of 247 zeptoseconds is wrong and the more accurate number is at least 353 zeptoseconds. Somebody tell the Nobel Committee they can Fedex my Prize to me. I'll be on the front porch doing science and watching football.

Tom and the Buccaneers beat their opponent, the Raiders. The Bucs are 5 - 2. Brady's contract with the Bucs is worth $50 million for two years. And he's married to super-model Gisele Bündchen, one of the highest paid models in the world. It's a tough life, Tom. You have our sympathies.

If reading this is confusing, you're not reading it right. You cannot switch back and forth between football and science. You must have the ball game and the science playing in your head at the same time. You can do it. Your brain has two halves, right? Now you know why. The left half gets the science and the right half gets the ballgame. Try it! I know it's difficult, but if you can manage to do it for a few seconds, then for those few seconds you'll get to know what living in my world is like!