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Uranium-234 has a half-life of 246,000 years. How did we measure that if the technology to do that hasn’t been around that long?

In: Chemistry

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The technology has been around since WWII. You can very accurately measure the rate of decay. If you measure the decay in a day, and it’s 5.56 x 10^-9 it’s a simple matter of multiplying that by 365 and dividing 0.5 by the result to get 246,000 as the half life.

Math.

Half life can be measured because it follows an exponential decay formula. once you have the rate you can work out the time until half of the units have decayed.

To do this you just measure how much has decayed within the time frame you have measured take several readings and you can plot the graph and extrapolate from there

In 246,000 years, half a sample will decay.

But if you have 492,000 atoms, there’s a good chance that one of them will go *this* year.

In a gram of uranium there’s ~10^21 atoms, and so even though any individual atom is likely to last for a hundred millennia, there will be a detectable rate of decay over a much shorter period of time.

You count how many decay events your Geiger counter picks up in an hour and extrapolate that out.

As others have already explained, you don’t need to measure the half-life of an element to know it.

You can measure it’s three-quarters-life too, or one-tenth-life, or nine-tenth-life, or even the nine-hundred-ninety-nine-thousand–nine-hundred-ninety-ninth-life, and get the information you need.

Half-life is just convenient because it’s straight in the middle.

The same way a police officer doesn’t need to watch your car for 80 miles to know you were doing 80 mph in a 60 mph zone. The speed at which you travel a shorter distance can be extrapolated to miles per hour. The amount of U-234 remaining after X time starting with a known quantity can be extrapolated to show at what point 50% would be expected to remain.

You don’t need to wait 246,000 years to know.

You just measure the decay of a know quantity over a known time period and extrapolate that curve out to when you hit 50% decay.

For very long half-lives you need a bigger sample and/or a longer test time and/or a more sensitive detector but unless the half-life is so long that you “never” get a decay, you can gather the data and plot the curve with relative ease.