Randomness of radioactivity

[SarahB]

How can radioactive decay be random if we can calculate aproximately when it will happen .
For example we know that an isotope will decay every 2 years by calculating the half life . Doesnt that mean that the decay is systematic rather than random because we can calculate when its guna happen .
Thanks

 

[phyzguy]

When an individual atom will decay is completely random. But each atom has a certain probability of decaying in a given time interval. So when I have large numbers of atoms, the number of decays vs time is very predictable. This is just like flipping a coin. Whether it comes up heads or tails is completely random. But it has a 50% probability of coming up heads or tails. So when I flip the coin 1 million times, there will be very close to 50% heads and 50% tails.

 

[Cutter Ketch]

I second phyzguy.

Also note that exponential decay is logical and natural. Suppose you start off with N nuclei. Each one has some possibility of decaying in the first second. If each has the same probability, then the probable number that do decay must be proportional to N. The exact number of decays isn’t guaranteed, but some number decay over the first second. Now there are fewer radioactive nuclei. Those that are left still have the same probability of decaying in the following second, but now there are fewer of them. The probable number of decays is fewer in the second second than the first not because the probability of decay for each nucleon is different, but rather just because there are fewer of them. Each second the number left ticks down and so the probable number that decay each second ticks down. Etc etc. The number of decays that are likely each second gets smaller and smaller second to second because there are fewer and fewer radioactive nuclei. That is the reason for the exponential decay in the radioactivity. Eventually there comes a time when only N/2 are left. That is the half life. It isn’t a behavior of the underlying probability for each nucleon each second. It is merely due to how many are left undecayed. The number left will be cut approximately in half every half-life time interval.

 

[SarahB]

When an individual atom will decay is completely random. But each atom has a certain probability of decaying in a given time interval. So when I have large numbers of atoms, the number of decays vs time is very predictable. This is just like flipping a coin. Whether it comes up heads or tails is completely random. But it has a 50% probability of coming up heads or tails. So when I flip the coin 1 million times, there will be very close to 50% heads and 50% tails.

So would we consider the randomness of the decay restricted within the time period of the predicted half life , so we don't really know exactly when its going to decay but its probably some time within this time frame.

 

[Cutter Ketch]

So would we consider the randomness of the decay restricted within the time period of the predicted half life , so we don't really know exactly when its going to decay but its probably some time within this time frame.

No, not quite. The half life is the 50-50 point. The probability that an individual nucleus will decay within one half-life time is 50%.

 

[phyzguy]

No, not quite. The half life is the 50-50 point. The probability that an individual nucleus will decay within one half-life time is 50%.

Right. So it might last 10 half-lives. Just like we might get 10 heads in a row.

 

[Cutter Ketch]

Right. So it might last 10 half-lives. Just like we might get 10 heads in a row.

And if you start with, say, a mole of radioactive nuclei, some lucky nuclei WILL last a many half-lives. The most likely time for the last one to go is N half lives where 2^N = 6.02E23 = 80 half-lives

All the U₂₃₅ on Earth was created in a supernova 6 billion years ago. The half life of U₂₃₅ is only 700 million years. The U₂₃₅ that is left has lasted almost 9 half lives and is only 1/2⁹ = 0.2% of the original amount.