Liquid Drop Model of the Nucleus

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Discussion Overview

The discussion revolves around the liquid drop model of the nucleus and its relation to the semi-empirical formula for atomic mass, specifically focusing on the instability of certain nuclei against beta and beta+ decay. Participants explore the factors influencing decay modes and the role of binding energy in determining these processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks to understand why some nuclei are unstable against both beta- and beta+ decay, suggesting a possible connection to the symmetry term in the liquid drop model.
  • Another participant questions whether the discussion pertains to stable nuclei or those that decay via k-shell electron capture.
  • A participant clarifies that they are referring to nuclei capable of undergoing both beta- and beta+ decay, indicating a belief that binding energy influences decay modes but does not specify which decay occurs.
  • A reference to copper-64 is made, highlighting its ability to decay through multiple processes, including beta- decay, beta+ decay, and k-shell electron capture, along with specific decay percentages and energy emissions.
  • It is noted that nuclei like copper-64 and vanadium-50 can beta decay in either direction if energetically favorable, with the condition that the parent nucleus is doubly odd and has high spin, creating a significant energy gap with respect to the daughter nuclei.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the factors influencing decay modes, and no consensus is reached regarding the specific mechanisms or conditions that determine whether a nucleus undergoes beta- or beta+ decay.

Contextual Notes

Some discussions involve assumptions about the symmetry term and binding energy without fully resolving how these factors interact with decay processes. The relationship between the liquid drop model and decay modes remains partially unclear.

venomxx
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Looking at the liquid drop model of the nucleus and the semi-empirical formula for the atomic mass of the nucleus.

I understand the formula but I'm trying to figure out why some nuclei are unstable against both beta- and beta+ decay. Any ideas? I assume it's something to do with the symmetry term?
 
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venomxx said:
Looking at the liquid drop model of the nucleus and the semi-empirical formula for the atomic mass of the nucleus.

I understand the formula but I'm trying to figure out why some nuclei are unstable against both beta- and beta+ decay. Any ideas? I assume it's something to do with the symmetry term?
Are you talking about stable nuclei, or those that decay only by k-shell electron capture?
 
Hi Bob,

Im talking about a nucleus that can undergoe either b+ or b- decay. There is a way of showing some can decay either way but i can't see it from the liquid drop model...the semi emperical formula can give mass and binding energy, the more i look into it the more i think that its the binding energy that will determine if it decays, but doesn't say whether it can decay by b+ or b-, or in my case both...

I hope that makes it a little clearer!
 
Here is what Wikipedia says about copper 64, an odd-odd nucleus that can decay by either electron (beta-) decay, positron (beta+) decay, or k-shell electron-capture. So Cu-64 decays 3 ways.

Wiki says
64Cu has a half-life of 12.701 ± 0.002 hours and decays by 17.86 (± 0.14)% by positron emission, 39.0 (± 0.3)% by beta decay, 43.075 (± 0.500)% by electron capture and 0.475 (± 0.010)% gamma radiation/internal conversion. These emissions are 0.5787 (± 0.0009) and 0.6531 (± 0.0002) MeV for positron and beta respectively and 1.35477 (± 0.00016) MeV for gamma.
 
Nuclei that can beta decay in either direction (Cu-64 is an example, as is V-50) will do so if it is energetically favorable to do so. This normally happens when the parent nucleus is doubly odd - high spin helps as well. This gives a large energy gap with respect to the daughters.
 
Cheers for the answers, helped me a lot!
 

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