How do I determine if a certain nuclear decay is allowed?

AI Thread Summary
To determine if a nuclear decay is allowed, it is essential to follow conservation laws, including baryon number, lepton number, electric charge, and mass-energy conservation. The example of Thorium-222 decaying into Oxygen-16 and Lead-206 raises questions about its validity despite conservation laws appearing to be satisfied. The mass difference calculation suggests the decay is allowed, as the total mass of the products is less than that of the original nucleus. However, the discussion emphasizes the importance of considering the mass differences between neutrons and protons in decay processes. Ultimately, understanding these conservation laws and mass considerations is crucial for determining the feasibility of nuclear decays.
Calleguld
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Hi, I am struggling with a question where they want me to determine whether or not three different decay are allowed.

From what I have understood all decays must follow a set of conservation law. These laws are:
1 Conservation of Baryon number
2 Conservation of Lepton number
3 Conservation of electric charge

This is very straight forward when you have simple decays like the decay of a neutron. Where you have:

n -> p+e+anti ve

But how does it work for nucleons?

For example:

Thorium-222 -> Oxygen-16 + Lead-206

This decay is not allowed as thorium-222 only decays with alpha-decay. But as far as I can see the laws are still followed.

1: 222 -> 16 + 206 = 222
2: 90 -> 8 + 82 = 90
3: 90-90 -> 8-8 + 82-82 = 0

What am I missing? please help!
 
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There's another requirement.
4. Mass+energy must be conserved.

Does Oxygen-16 + Lead-206 have more mass than Thorium-222? If so, then the decay is not allowed.
 
DuckAmuck said:
There's another requirement.
4. Mass+energy must be conserved.

Does Oxygen-16 + Lead-206 have more mass than Thorium-222? If so, then the decay is not allowed.

I forgot to add that law.

The mass difference is: 222.018468u - (205.974465u + 15.994914u) = 0.0491u

Which would suggest that this decay is allowed.

Thanks for the answer though!
 
Are you taking into account the difference in mass between neutrons and protons? Recall that neutrons are a bit heavier than protons.
 
DuckAmuck said:
Are you taking into account the difference in mass between neutrons and protons? Recall that neutrons are a bit heavier than protons.

Yes that difference is accounted for. I got the masses from this site/paper https://www-nds.iaea.org/amdc/ame2012/mass.mas12
 
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