Count to an appreciation of a 5c piece

By Associate Professor Allan Blackman

This article was orignally published in the Otago Daily Times on Monday 12 January 2004.

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Is it just me, or are the years getting shorter? Even though it seems that time passes more rapidly the older one gets, a check of the calendar assured me that 2003 did, in fact, contain 365 days.

That's 8760 hours, or 525,600 minutes, or 31,536,000 seconds. If you're an average Kiwi, you can expect to live for about 80 years, which translates to about 2,500,000,000 (two-and-a-half billion) seconds, give or take the odd leap-year. In human terms, 2,500,000,000 is an enormous number, equating to roughly half of the population of the earth. However, in chemical terms, it's not even a drop in a bucket.

Let's assume we can count individual atoms. How long would it take us to count all the atoms in a 5c piece if we counted one atom every second? Months? Years? Decades? Have a guess before you read any further.

In order to calculate the number of atoms that we'll be counting, we need to know that a 5c piece is made up of 75% copper and 25% nickel, and that it weighs 2.83 grams. So let's assume we're average Kiwis and we count the atoms in the 5c piece at a rate of one every second for 80 years. As I've shown above, by this time, we would have counted about two and a-half billion atoms. But that's not nearly enough.

Let's now assume that we can live to a Methuselah-like age — 969 years, to be exact. Counting one atom per second for this length of time would get us to about 30 billion atoms. But we're not there yet.

One of the oldest trees on Earth, a bristlecone pine tree in California (coincidentally, called Methuselah), has an estimated age of 4700 years. An atom a second for that length of time gives us about 148 billion atoms.

You'd think we'd be getting close to counting all the atoms in the 5c piece by now, but you'd be wrong. We're not even 1% of the way there. In fact, we're not even anywhere near 1%. We're obviously going to be counting for a while.

Earth is thought to be about 4.6 billion years old. So let's assume we've been around since the formation of the earth, and we've been diligently counting the atoms in the 5c piece at one atom per second (of course, these coins were first minted in 1967, so our experiment might be somewhat flawed). After this time, we'd be old, out of breath, and we would have counted around 145 quadrillion atoms. Or, in other words (or numbers), 145,000,000,000,000,000 atoms. Surely, we must have counted all the atoms by now? Nope! Still not even close. In fact, the atoms we've counted by this time would weigh a total of 15 micrograms; probably just enough for us to see with the naked eye, but nowhere near the number in our 5c piece.

Even if we counted 1000 atoms per second from the time of the formation of the earth, we would still be only about 0.5% of the way there.

There are approximately 27,400,000,000,000,000,000,000 atoms in a 5c piece and, at an atom per second, it would take us about 800 trillion years, or roughly 70,000 times the age of the universe to count these. This is a number of truly incomprehensible magnitude. More incredible still, if we stacked these atoms one on top of another, the resulting chain would go around the earth about 100,000 times.

Makes you look at the humble 5c piece in a whole new light, really, doesn't it?