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

• Calleguld
In summary, decay follows a set of conservation laws, including conservation of baryon number, conservation of lepton number, conservation of electric charge, and conservation of mass and energy. While simple decays like the decay of a neutron follow these laws easily, more complex decays, such as Thorium-222 decaying into Oxygen-16 and Lead-206, require further consideration. The mass difference between the reactants and products must also be taken into account, with the understanding that neutrons are slightly heavier than protons. In this case, the decay is allowed as the mass difference is within the allowed range.
Calleguld
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:

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

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.

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

## 1. What is nuclear decay?

Nuclear decay is the process in which an unstable atomic nucleus emits particles or energy in order to become more stable.

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

Nuclear decay is allowed if it follows the laws of conservation of energy, conservation of momentum, and conservation of electric charge. In other words, the total energy, momentum, and charge before and after the decay must be the same.

## 3. What are the factors that determine if a nuclear decay is allowed?

The factors that determine if a nuclear decay is allowed include the stability of the nucleus, the energy released during the decay, and the conservation laws mentioned above.

## 4. What is the difference between allowed and forbidden nuclear decays?

An allowed nuclear decay is one that follows the conservation laws and is energetically favorable, while a forbidden nuclear decay is one that violates the conservation laws and is energetically unfavorable.

## 5. How can I experimentally determine if a nuclear decay is allowed?

Experimental techniques such as beta decay and gamma spectroscopy can be used to detect and measure the particles and energy released during a nuclear decay, allowing scientists to determine if it is allowed based on the conservation laws.

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