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

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!

## Answers and Replies

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.

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.

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