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tmeunknown · Oct 12, 2010, 11:42 AM

Starting with the number two, multiply it by itself, then take that number and multiply itself, etc, etc.
It's been said that if a computer counted a million atoms a second that it would take billions of years to count the amount of atoms in a gram of any element. Could you count the amount of atoms this way in a year maybe?

DrBob1 · Oct 12, 2010, 01:20 PM

This is to show you how large Avogadro's number really is.
Sixty seconds in a minute, sixty minutes in an hour, 24 hours in a day, 365.25 days in a year equals, call it 3.16 x 10^7 seconds. So it will take only 2 x 10^16 years. I don't think I'll wait!

Unknown008 · Oct 13, 2010, 06:29 AM

I'm not sure what you're looking for, but I'm taking your "take a number, multiply it by itself, take that result and multiply it by itself again and again".

The number of atoms counted after t seconds will be:

$2^{2^t}$

Check it. After 2 seconds, we have (2x2) = 4
Then multiply that by itself, giving 16.

$2^{2^2} = 16$

3 seconds, 16x16 = 256

$2^{2^3}= 256$

4 seconds 256 x 256 = 65536

$2^{2^4} = 65536$

Ok, the equation is good.

In 1 gram of H atoms, there are 6.02x10^23 atoms.

$6.02\times10^{23} = 2^{2^t}$

$2^t = 78.99$

$t = 6.30$

Hmm, it takes only 6.3 seconds :rolleyes:

And the larger you get, the less number of atoms you have...

Now, taking a million atoms a second, you will have $\frac{6.02\times10^{23}}{1\times10^6} = 6.02 \times 10^{17} s \approx 2\times10^{16} years$