# radioactive decay and half life

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when you say radioactive decay is random do you mean at one time it decays faster and another Time it decays slower

is radioactive decay spontaneous as in it isn't affected by external factors?

Also if it's random how can you say that for example every 10 days, the activity decreases by half.isnt it too specific when it's random?

idk

is radioactive decay spontaneous as in it isn't affected by external factors?

Also if it's random how can you say that for example every 10 days, the activity decreases by half.isnt it too specific when it's random?

idk

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It is spontaneous. You cannot predict exactly when a nucleus will decay.

But, there is a certain probability that it will decay. The decay constant λ is a measure of this.

If you have a

In fact, the half life T

This is observed to happen.

That varies from material to material.

Clearly, the time it will take half of them to decay depends on the chance of the nucleus decaying in the first place.

If the probability λ is small, it will take longer for half the sample to decay.

If the probability λ is high it will take a shorter time for half the sample to decay.

There is an equation that relates λ and T

The activity of the sample depends on how many active nuclei are present, so if half have decayed, the activity is also reduced by half.

It all depends on there being a very large number of nuclei present. In this case then, it is possible to predict the behavior of the sample based on this idea of probability of decay, even though the decay event is random.

An analogy would be throwing coins.

We cannot predict if it is going to be head or tail, but we do know that there is a 0.5 probability (50% chance) of it being a head. This is indeed random.

But if I have enough coins and throw them all, I know that about half of them will be heads and half tails. The more coins I have, the closer it will be to half heads and half tails,

In the case of a radioactive sample we have a lot (millions) of nuclei.

But, there is a certain probability that it will decay. The decay constant λ is a measure of this.

If you have a

**large enough**number nuclei together, a certain fraction of them will decay in a particular length of time.In fact, the half life T

_{1/2}is that time after which half of them would be expected to decay.This is observed to happen.

That varies from material to material.

Clearly, the time it will take half of them to decay depends on the chance of the nucleus decaying in the first place.

If the probability λ is small, it will take longer for half the sample to decay.

If the probability λ is high it will take a shorter time for half the sample to decay.

There is an equation that relates λ and T

_{1/2}The activity of the sample depends on how many active nuclei are present, so if half have decayed, the activity is also reduced by half.

It all depends on there being a very large number of nuclei present. In this case then, it is possible to predict the behavior of the sample based on this idea of probability of decay, even though the decay event is random.

An analogy would be throwing coins.

We cannot predict if it is going to be head or tail, but we do know that there is a 0.5 probability (50% chance) of it being a head. This is indeed random.

But if I have enough coins and throw them all, I know that about half of them will be heads and half tails. The more coins I have, the closer it will be to half heads and half tails,

In the case of a radioactive sample we have a lot (millions) of nuclei.

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(Original post by

when you say radioactive decay is random do you mean at one time it decays faster and another Time it decays slower

is radioactive decay spontaneous as in it isn't affected by external factors?

Also if it's random how can you say that for example every 10 days, the activity decreases by half.isnt it too specific when it's random?

idk

**student144**)when you say radioactive decay is random do you mean at one time it decays faster and another Time it decays slower

is radioactive decay spontaneous as in it isn't affected by external factors?

Also if it's random how can you say that for example every 10 days, the activity decreases by half.isnt it too specific when it's random?

idk

For the random nature of radioactivity, it is best to think of it in terms of there being no way to determine with nuclei in a sample is going to be the next one to decay. All nuclei of the same type are as likely to decay as each other. You can only say that they have an equal probability of decaying in a particular time, not that you can tell which is going to be the ones that do so.

If you have a material with a half-life of 10 days, then it almost won't be the case that exactly half of it has decayed after 10 days, so the activity will not have dropped by exactly a half. The mathematical model is a theoretical indication of what is most likely to happen, not a 100% reliable prediction as to what will happen. For example, if you throw 36 fair dice, we would expect on average that 6 of them will come up as a 6, but this isn't going to happen every time.

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