Beta Decay: Why Isomeric State Has Long Half-Life

In summary, the half life for the isomeric state at 140 kev which decays by gamma emission is comparable to the original state (Mo) decaying to the allowed excited state of Tc. Any tips on what approach I can take to show this?
  • #1
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Please look at the attached file.

The first part of the question: why it doesn't decay to the GS. I think that's simply because the nuclear spin changes by 4 and therefore this decay is very supressed.

But how "is it possible for the isomeric state at 140kev which decays by gamma emisson, to have a half life of several hours." (ie. a half life comparable to the original state (Mo) decaying to the allowed excited of Tc. Any tips on what approach I can take to show this?

Thanks.
 

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  • #2

It can decay into its ground state, however it is less probable, however the decay pathways are generally toward the next lower energy spin state until the ground state is reached.

The reason why it is 'negligible' is because of the extreme energy difference between the energy levels of 1.21 Mev -> 0.14 Mev, where the 0.14 Mev energy level is extremely close to the ground state energy level. The spin states are also a factor, the difference in energy levels in a decay of one spin state into its ground spin state.
 
  • #3
Orion1 said:
The spin states are also a factor, the difference in energy levels in a decay of one spin state into its ground spin state.

thanks for your reply Orion1. I would have thought the difference in spin states is the main reason - I mean nuclear spin changes by 4 (if there was a transition to the ground state). Its the fourth forbidden transition so it would be very, very supressed.

What about the second part of the question: any thoughts on how to show it has a half life of several hours?
 
  • #4


In simplest terms, if the decay slope is linear, the half life is proportional to the difference in energy between the two spin states.

[tex]\frac{T_{\frac{1}{2} a}}{T_{\frac{1}{2} b}} \propto \frac{Q_{\beta1}}{Q_{\beta2}}[/tex]

[tex]T_{\frac{1}{2} b} \propto T_{\frac{1}{2} a} \left( \frac{Q_{\beta2}}{Q_{\beta1}} \right) = 66 \; \text{hrs} \left( \frac{0.14 \; \text{Mev}}{1.21 \; \text{Mev}} \right) = 7.636 \; \text{hrs}[/tex]

[tex]\boxed{T_{\frac{1}{2} b} = 7.636 \; \text{hrs}}[/tex]

The remaining difference being due to the effects of differential spin states.

[tex]\boxed{T_{\frac{1}{2} b} = 7.636 \; \text{hrs} - \Delta S \cdot 0.409 \; \text{hrs}}[/tex]
 
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  • #5
presently my research filed is beta spectroscopy in light nuclei near the drip line.
If you are interested in it, please contact with me,.
 
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  • #6
Many thanks Orion1:)

monkey this is a past finals question. I'm just revising for exams!
 

1. What is beta decay?

Beta decay is a type of nuclear decay where an unstable atomic nucleus releases a beta particle (either an electron or a positron) and transforms into a different element.

2. What is an isomeric state in beta decay?

An isomeric state in beta decay is a specific excited state of a nucleus that has a long half-life compared to other excited states. It is also known as a metastable state.

3. Why does the isomeric state have a long half-life?

The isomeric state has a long half-life because it is energetically favored to remain in this state rather than decaying to a lower energy state. This is due to quantum mechanical effects and the specific arrangement of protons and neutrons in the nucleus.

4. How is the isomeric state formed?

The isomeric state is formed through a nuclear reaction, such as beta decay, where the nucleus absorbs energy and transitions to a higher energy state. This can also occur through other processes such as gamma decay or neutron capture.

5. What are some applications of isomeric states with long half-lives?

Isomeric states with long half-lives have various applications in nuclear medicine, nuclear energy, and scientific research. They can be used as radioactive tracers to study biological processes, as well as in the production of medical isotopes for diagnostic imaging and cancer treatment. They are also useful in controlling nuclear reactions in nuclear power plants and in studying fundamental properties of nuclear matter.

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