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Beta Decay question 
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#1
Jun308, 10:43 AM

P: 230

Please look at the attached file.
The first part of the question: why it doesn't decay to the GS. I think thats 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. 


#2
Jun308, 11:09 AM

P: 989

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
Jun308, 11:18 AM

P: 230

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


#4
Jun308, 08:49 PM

P: 989

Beta Decay question
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] 


#5
Jun408, 06:49 AM

P: 1

presently my research filed is beta spectroscopy in light nuclei near the drip line.
If you are interested in it, please contact with me,. 


#6
Jun408, 08:57 PM

P: 230

Many thanks Orion1:)
monkey this is a past finals question. I'm just revising for exams! 


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