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# Half-life plot

Definition of half-life and graphing the decay of phosphorus-32. Calculating how much phosphorus-32 remains after 57.2 days.  Created by Jay.

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• Well if the radioactive substance keeps getting halved; then does that mean that it never really gets depleted? like from 1 to 1/2, then 1/4,1/8,1/16.....
• Theoretically, that's correct.
In practice, once the numbers get too low, we are no longer able to detect the substance, and we then say that it has disappeared.
Many scientists use an arbitrary cut-off point and say that a radioactive substance has been depleted after 20 half-lives. By that time, only one-millionth of the original sample remains.
• Well, I can imagine how half life of radioactive phosphorus is measured, it's not that long. But how the half life of, for example, uranium isotopes was found? It is measjred in billion years...
• That is not needed because we don't actually measure the half-life, we measure the decay constant. From that it is a simple calculation to get the half-life (or any other fraction you might care to use).

The equation is:
N = N₀ e^(−λt)
Where N is the final amount of the substance, N₀ is the initial amount of the substance, t is time, and λ is the decay constant.
So we just pick some convenient amount of time, measure the other variables and compute λ. Once we know λ, we can compute the half-life or any other convenient fractional life.

λ can also be determined by other methods which involve counting the number of decays per unit time for a given quantity of the material (this is especially useful for radioactive isotopes that exist in trace amounts).

The point being is that half-life is just an easily understood number that we can use for reference. We really measure the λ or the related quantity τ. called "mean lifetime".
• why half life is different for different elements?
• Half life depends on the protons and neutrons, and different isotopes have different number nucleons
• Does an element have to be radioactive for it to decay?
(1 vote)
• That's what radioactive means - that it decays.
• So using this chart we see that after the first half life happened in 14.3 days, and half life 2 happened in 28.6 days, which confirms that that the half life 3 will occur in 42.9 days.

Does this means that only 1/8th of the original material is remaining? Is this what actually happens or is this some sort of Achilles and the Tortoise thing?
• How do I find the half life of something from the exponential decay equation? (ede = y=sv(df^x) where sv is the start value, and df is the decay value)
• If half a substance decays in one years time why is it incorrect to expect the other half to decay in one more year?
• Decay is a probabilistic occurrence. It is better to think of it as how long does it take for any given atom to have a 50% chance of decaying. If any atom doesn't decay in that half-life, it still has a 50% chance of decaying over the next half-life. The fact that it didn't decay in the first half-life doesn't increase the probability of decay.
• Why decay rate, which is directly proportional to no of atoms present, is constant always constant? As if we see in other random events the highest probability is near to mean value. For example if we take a large numbers of people, they may not decay (die) by above rule, instead most of the people will die near average age.
(1 vote)
• I think you might be mixing up the number of atoms that decay with the percentage of atoms in your sample that decay. If something has a half-life of one year and you have 100 atoms of it, then in one year 50 of them will have decayed. But if you have 200 atoms, then in one year 100 of them will have decayed. Different numbers of atoms decayed, but either way 50% of the sample has decayed.
Hope this helps!