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### Course: Class 12 Physics (India)>Unit 13

Lesson 3: Half life and decay rate

# 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.

## Want to join the conversation?

• 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?
• Does any substance with a non first order decay reaction exist ?? ( so the half life changes with its quantity)
• For a second order or higher, the decay process itself has to somehow depend on the presence of other molecules and interact with it. This kind of a mechanism is not true for most of spontaneous radioactive decay. But in the presence of any external stimulant, the situation can change, for example in uncontrolled nuclear fission. It is not a true spontaneous decay process, but the nucleus splits in the presence of another projectile.
• 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.
• 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)
• since its constantly being cut in half does that mean that it will never reach zero?
(1 vote)
• When you reach the limit of a single atom it either decays or not there is no half of an atom of an element.