Does K-40 Capture Electrons With Orbital Angular Momentum?

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In summary, K-40 captures electrons from the environment to form Ar-40. The spins of the electron and neutrino combine to at most 1, leaving 3 spin units to handle. Orbital angular momentum is not found in K-shell, so K-40 preferentially captures outer electrons with angular momentum.
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snorkack
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TL;DR Summary
Handling of spin in electron capture
K-40 often captures electrons. This is why Earth atmosphere is full of Ar-40.
Where does K-40 capture electrons from?
The problem is that K-40 has spin 4. Ar-40 has spin 0.
How are the 4 spin units handled?
The spins of the electron and neutrino combine to at most 1. This leaves 3 spin units to handle. How?
By emitting the neutrino with an orbital angular momentum? Or by capturing electron with orbital angular momentum?
Orbital angular momentum is not found in K-shell (it is 1s orbital, no angular momentum). Does K-40 preferentially capture outer electrons which do have angular momentum?
 
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snorkack said:
Summary: Handling of spin in electron capture

K-40 often captures electrons. This is why Earth atmosphere is full of Ar-40.
About 11% of K-40 decays are due to electron capture.
I would not say that the atmosphere is full of Ar-40, that is a bit of an exaggeration.

snorkack said:
Where does K-40 capture electrons from?
From the electons bound to the nuclei, they have a small probability to be located close enough to the nucleus such that the process ##e^- + p \to n + \nu + \gamma## occurs.
Neutron remain in nucleus, Ar-40 is formed.
The photon is not emitted directly, the Ar-40 is formed in an excited state with some non-zero angular momentum. The emission of the photon will carry away that excess angular momentum so that the final state nuclei has spin 0. It is also thanks to this photon that we can use K-40 for radioactive dating (give it a try next valentines day!)
snorkack said:
Does K-40 preferentially capture outer electrons which do have angular momentum?
No, because such electron states have extremely low probability to be near the nuclei.

1658872245440.png

Nice picture from: https://www.radioactivity.eu.com/site/pages/Potassium_40.htm
 
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malawi_glenn said:
we can use K-40 for radioactive dating (give it a try next valentines day!)
Har! Har! Har! :rolleyes:
 
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ohwilleke said:
Har! Har! Har! :rolleyes:
Oh honey you look radiant!
 

1. What is K-40 and why is it important in electron capture?

K-40 is a radioactive isotope of potassium that is naturally found in the Earth's crust. It is important in electron capture because it has a high probability of capturing electrons, which can lead to the production of a more stable element.

2. How does K-40 capture electrons with orbital angular momentum?

K-40 captures electrons with orbital angular momentum through a process called electron capture. In this process, an electron from an inner shell of the atom is absorbed by the nucleus, resulting in the emission of a neutrino and the formation of a more stable element.

3. What is the significance of orbital angular momentum in electron capture?

Orbital angular momentum is significant in electron capture because it determines the probability of an electron being captured by the nucleus. The higher the orbital angular momentum, the higher the probability of electron capture.

4. Can K-40 capture electrons with any other type of momentum?

No, K-40 can only capture electrons with orbital angular momentum. This is because electron capture is a specific process that involves the absorption of an electron from an inner shell, and orbital angular momentum is the only type of momentum that an electron in an inner shell possesses.

5. How does the capture of electrons by K-40 affect the stability of an atom?

The capture of electrons by K-40 can result in the production of a more stable element. This is because the addition of an electron to the nucleus can balance out the positive charge of the nucleus, making it more stable. Additionally, the emission of a neutrino during electron capture also helps to stabilize the atom.

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