Spontaneous Calculation

Sometimes the most fun in class is when it skews off in a wildly unplanned direction.  Sometimes it’s a big skew, sometimes a little detour.

We have been studying particle physics topics in class for the past couple of weeks, including a trip to Kansas State University for a QuarkNet Master Class.  We were discussing in class that the data we used to determine the mass of the top quark came from the Tevatron at Fermilab, and that it was from a proton-antiproton collision.

Some of my students were a little incredulous at the thought of antimatter, asking “Isn’t that a science fiction thing?”  Yes, yes it is, but it is also very real.  There just isn’t much of it around, and that why exactly we have almost exclusively matter and no antimatter is a Really Good Question We Haven’t Solved Yet.  Although there is no significant amount of antimatter naturally occurring anywhere in the universe, such as no antimatter stars or planets or nebulae that we are aware of, we can manufacture it.

Manufacture it?  Yes, we can.  Particle colliders like the LHC do it all the time.  It is even created naturally in tiny quantities through certain types of radioactive decay.

“So,” one of my students asked, “how much would a pop can full of antimatter cost?”

Hmm.

That is a good question that deserves an answer.  After mentioning that I’m pretty sure we have not produced a pop-can full of antimatter of any kind in total, I was off to find the answer.

A Google search quickly came up with a NASA site from 1999 that quoted the cost of antihydrogen at $62.5 trillion per gram.  Sure, that’s 1999 dollars, but it will work for our purposes.

We needed a few other factors, like the density of liquid hydrogen (70.99 g/L), and the conversion from 12 fluid ounces to liters (12 Fl.oz. = 0.354882 L).  And with a quick calculation, we had our answer:  $1.57E15

That’s $1,570,000,000,000,000.

Over one and a half quadrillion dollars.

The discussion swayed to how many pop cans of antimatter you could buy if you could sell the entire planet, but by then the period was winding down and it was time to go.

It leaves me wondering…by the end of my teaching career, how far that cost for a pop-can full of antihydrogen might fall.