# Radioactivity, disintegrations and Half Life

Hi,

My Physics textbook talks about a nucleus disintegrating. What does this mean? I understand that the nucleus will emit either an alpha, beta or gamma ray but surely the nucleus still remains after this? Does the term disintegrate just mean than the nucleus has got smaller and become a new element? Isn't this what decay means?

The textbook also gives the definition of Half Life as the time for the mass of the isotope to half. I thought it was the time for half the unstable atoms to decay. Whats the difference? A radioactive substance wont decay (or disintegrate) until it becomes nothing (zero mass), will it?

Any help would be great.

Thanks

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QuantumPion
Gold Member
Hi,

My Physics textbook talks about a nucleus disintegrating. What does this mean? I understand that the nucleus will emit either an alpha, beta or gamma ray but surely the nucleus still remains after this? Does the term disintegrate just mean than the nucleus has got smaller and become a new element? Isn't this what decay means?
Yes.

The textbook also gives the definition of Half Life as the time for the mass of the isotope to half. I thought it was the time for half the unstable atoms to decay. Whats the difference? A radioactive substance wont decay (or disintegrate) until it becomes nothing (zero mass), will it?

Any help would be great.

Thanks
You are correct, and your textbook definition, as written, is wrong. The average lifetime of a radioactive nucleus is $\frac{1}{\lambda}$. The half-life is the time it takes for half of the sample to decay, which is $\frac{ln\:2}{\lambda}$.

russ_watters
Mentor
The textbook definition is correct, it is just confusingly worded. It is referring to the mass of the original isotope. After a half life, you're left with half of that isotope.

QuantumPion
Gold Member
The textbook definition is correct, it is just confusingly worded. It is referring to the mass of the original isotope. After a half life, you're left with half of that isotope.
No it is not just confusing, it is outright wrong. The mass of the isotope does not change (this is a fixed physical parameter). The mass of the nucleus which decays does change - but not by half. It changes by the mass of the decay particle and energy difference. It is only the count of a large sample of atoms which decreases by half after one half life.

russ_watters
Mentor
If the count of atoms of an isotope drops by half, the mass of that isotope - not the atomic mass, the total mass - has also dropped by half.

Thanks for the replies. Sounds like I haven't asked a stupid questions!

Russ you say...

"If the count of atoms of an isotope drops by half, the mass of that isotope - not the atomic mass, the total mass - has also dropped by half."

I understand that but why would the actual count of atoms reduce by half? I thought that the atoms themselves simply decay, the mass of the nucleus would reduce, but the atom would remain. Albeit now a different element or isotope. If half the atoms have decayed then surely this wouldn't mean the entire sample has reduced it's mass by half?

I feel like i'm not understanding something quite fundamental to radioactive decay. Does everyone agree that disintegration and decay are the same thing and the atom still remains afterwards?

Many thanks

russ_watters
Mentor
"If the count of atoms of an isotope drops by half, the mass of that isotope - not the atomic mass, the total mass - has also dropped by half."

I understand that but why would the actual count of atoms reduce by half?
If half of the atoms of an isotope decay, you are left with half of the atoms of that isotope. The other half are now a different atom. Consider:

If you have 1 kg of a certain isotope and wait for one half life, how much of that isotope do you now have?

Ah!

I get it. More of an problem understanding the language that the Physics itself. I hate that!

So after one half life of 1kg of a certain isotope 500g of that same isotope would remain but the total mass of the material is going to be much greater than 500g!