Beta/gamma decay probabilities

In summary, the conversation was about the beta decay of 212Pb and the probability of it leading to the second excited state of 212Bi at 238.6 keV and the probability of it being accompanied by the emission of a 238.6 keV gamma ray. The difference between these two values was discussed, with the conclusion that they are different questions depicting different situations. The conversation also touched on using the binding energies of bismuth to identify emissions and the mystery of how nuclei go to the ground state without emitting a gamma photon.
  • #1
CloudNine
15
3
Hi all,

I have received this following question which I can't really figure out all the way to the end:

Consider the beta decay of 212Pb:
צילום מסך 2021-10-31 ב-23.15.52.png

* What is the probability that the decay leads to the second excited state of 212Bi at 238.6 keV?
This is straight forward - from nndc NuDat, it seems that the answer is simply 81.5%:

*What is the probability that the beta decay is accompanied by the emission of a 238.6 keV gamma ray? Explain (qualitatively) the difference between this value and your answer to (a).
Here, the answer is, if I'm not mistaken (but here's my difficulty) is like so:
Lets define:
A - beta decay to the second excited state of Bi-212
B - gamma decay with 238.6 KeV
Since decaying with 238.6 KeV can only happen from the 2nd excited state of Bi-212, the events are dependent. Thus:
P(B∩A)=P(B|A)P(A)=0.436*0.815=0.35534

I don't understand "what is the difference" between this value and the answer to (a). These are different questions, depicting different situations..

*Google the binding energies of the bismuth K, L, M and N shells. Use this information and the Nudat database to identify the main emissions which solve the mystery of (b).
Totally lost it! What mystery? :( Is this the correct table to use? What does it give?

צילום מסך 2021-10-31 ב-23.25.11.png
 

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  • #2
I think the problem asks indirectly how the other 56% of the nuclei go to the ground state if they don't emit a gamma photon.
 
  • #3
mfb said:
I think the problem asks indirectly how the other 56% of the nuclei go to the ground state if they don't emit a gamma photon.
Yes I think you are right. I've dived into the theoretical explanations again and things make more sense now, and so I'm able to compile a coherent answer (hopefully).
Thanks!
 

What is beta/gamma decay?

Beta/gamma decay is a type of radioactive decay in which an unstable atomic nucleus releases energy in the form of beta particles (electrons) and gamma rays.

What is the difference between beta and gamma decay?

Beta decay involves the emission of beta particles from an unstable nucleus, while gamma decay involves the release of high-energy photons (gamma rays) from an excited nucleus.

How are beta/gamma decay probabilities calculated?

Beta/gamma decay probabilities are calculated using mathematical models based on the properties of the unstable nucleus, such as its half-life and decay constant.

What factors affect beta/gamma decay probabilities?

The half-life of an unstable nucleus, its decay constant, and the type of decay (beta or gamma) are all factors that can affect beta/gamma decay probabilities.

Why is understanding beta/gamma decay probabilities important?

Understanding beta/gamma decay probabilities is important for predicting the behavior of radioactive materials, as well as for applications in fields such as nuclear energy and medicine.

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