How do scientists know the half life of a substance when the half life is longer than the time we have known about the substance?
In: Physics
The same way you that they say *a watch loses one second every thousand years*. They don’t wait a thousand years! They see how much it loses over an hour/day/whatever and extrapolate to units that are more relatable.
Observation and mathematical estimates. Even for very long half lives, if the decay is observed to happen at a consistent and predictable rate over long periods, then the half life can be calculated from the measured and observed data.
Even if the half-life of Uranium-238 is 4.5 billion years some time will decay now and some in 10 billion years. Every moment U-238 atoms have some chance of decaying it is just very low. It also has no memory so the chances of a single atom decay this minute is the same as for the next minute and so on until it decays. Each atom is independent so neighboring atoms have no effect on it.
Atmos is very small so you can have huge amounts so even if the chances of one atom decay is very small if you have enough som will decay.
If you have one mole of U-238 atoms that have a mass of 238 grams you have 6.02214076×10^23 atoms. That is a 6 with 23 zeros after. If half will decay in 4.5 billion years 3*10^23 atoms will decay during that time.
4.5 billion is 4.5*10^9 so you have 3*10^23 / 4.5*10^9 =6.6*10^13 decays per year. Per second you have 6.6*10^13 /(365*24*60*60)=2*10^6 or 2 million atoms that decay per second.
You can calculate the half-life if you know the number of decays per unit of time today and the number of atoms in the sample.
The math is a simplification with content decay for a half-life, in practice, it will be more at this moment and less over time. It will be an exponential function but assuming a constant decay rate is a lot simple and get the point across.
Math!
The half-life is constant so by measuring how much stuff you have at time A and how much stuff you have at time B you can solve for the half life
If I have a blob of substance X which gives off 100,000 beta particles per hour at the beginning bit only 99,900 per hour 10 days later then you can solve for the half-life
Amount at time B = Amount at time A x e^(-(time difference)/half life
Since we have the amount at time B (99,900) and at time A (100,000) and we know the time difference is 10 days then Wolfram tells me the half-life is 9995 days or about 27 years
Math.
The half life doesn’t mean that after the half life is up half of the stuff disappears immediately. It is a continuous process.
If you have enough of a material you can measure even small changes over time and then use these to calculate what the change would be over longer time.
Half life is just a convenient label for comparison, not necessarily what is measured in all cases.
The half life is just a standard measure of how fast unstable isotopes decay. It is possible to convert between half time and say 90%time or 99.9%time and back again. So you measure how many isotopes decay in say one hour versos how many isotopes there are in the sample and then you can extrapolate from this the half time of the specific isotope in millions of years.
A simple equation can be used to get it. It is just all maths (mostly rate changes(d/dx) and integration)
We can precisely measure the radiation of a substance and check how much times it takes for it to lose 1% of radiation and with that and a little bit of math we can calculate the half life.
By studying the radiant particles that are produced as it decays and analyzing the way it decays and the elements that are produced. Basically it’s math and equations.
To make an analogy, imagine that we know that inside of a box are 100 mouse traps with ping pong balls balanced on them, and that each time a mouse trap changes states, a ping pong ball is lost (as it’s tossed off the trap). We can’t see inside the box and so we can’t see how quickly this happens on it’s own. But there is a funnel at the bottom with a hole cut out, and we can count how often the ping pong balls are ejected. By knowing the average of how quickly balls are radiated, and how many traps were in the box to begin with, we can work out how quickly they will decay.
For simplicity sake, imagine that element A becomes element B with no intermediate elements. If you know how many atoms are in your sample, what they decay into and the mass of the decayed atoms, then you can measure the radioactive counts to determine how quickly it’s happening. From that you can estimate on average how long it would take for that sample to convert half of it’s atoms to the new element.
It helps to think about what radiation actually is. It’s the bits that are lost when a heavier element decays into a lighter element. It’s made up of the bits and pieces that don’t fit in the new element and are ejected or radiated out. Alpha radiation for instance is a helium nucleus. Beta radiation is basically an electron (or positron). Gamma is basically really energetic light. There is also neutron radiation which is exactly what it sounds like.
The point is that by knowing the equations for radioactive decay, we know what will be radiated when it occurs, and we can then count how often that radiation is occurring in order to measure the speed it’s decaying. All of that information together gives us the half life.
In real life, there are often several elements that a heavy element will decay into, and those elements may in turn be unstable and also decay. There are also different kinds of radiation depending on what is decaying. There are also neutrons which can actually collide with non radioactive elements, and make them radioactive. So the math can get pretty complex.
[this image](https://qph.fs.quoracdn.net/main-qimg-ad2ea8c669e7138e5ee166947866c71e.webp) shows how Uranium 235 decays into several different elements. Notice that each is linked with the symbols for alpha and beta. This shows what particle is given, and what the new element is, how that element decays and what particles it gives. Some give both alpha and beta particles and there is more than one way they can decay (more than one path from uranium to lead). Notice there are some common problematic elements there like Radon, which can be produced naturally as uranium decays. It’s a gas and collects in pockets under ground and it can seep up to the surface, which is why in areas of the country where there are uranium minerals, radon detectors are so important in places like basements.
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