Liquid Drop Model of the Nucleus

In summary, Cu-64 can decay by beta- or beta+ decay, depending on the energy gap between the parent and daughter nuclei.
  • #1
venomxx
39
0
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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  • #2
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?
 
  • #3
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!
 
  • #4
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.
 
  • #6
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.
 
  • #7
Cheers for the answers, helped me alot!
 

Related to Liquid Drop Model of the Nucleus

What is the Liquid Drop Model of the Nucleus?

The Liquid Drop Model of the Nucleus is a theoretical model used to describe the structure and behavior of atomic nuclei. It was proposed in the 1930s and is based on the assumption that the nucleus behaves like a drop of incompressible liquid, with a surface tension that holds it together. This model is useful in understanding nuclear stability, radioactive decay, and nuclear fission.

What are the main assumptions of the Liquid Drop Model?

The main assumptions of the Liquid Drop Model are that the nucleus is made up of nucleons (protons and neutrons) which are held together by a strong nuclear force, similar to the surface tension of a liquid. It also assumes that the nucleons are arranged in a spherical shape and that the nucleus has a constant density throughout.

How does the Liquid Drop Model explain nuclear stability?

The Liquid Drop Model explains nuclear stability by considering the balance between the attractive strong nuclear force and the repulsive electrostatic force between protons. Nuclei with a higher number of protons (high atomic number) tend to be less stable due to the increased electrostatic repulsion, while nuclei with a balanced number of protons and neutrons (magic numbers) are more stable.

What is the significance of the Liquid Drop Model in nuclear fission?

The Liquid Drop Model is significant in understanding nuclear fission, which is the splitting of a heavy nucleus into two smaller nuclei. This model predicts that nuclei with an atomic number greater than 83 (such as uranium and plutonium) are more likely to undergo fission due to their increased instability caused by the electrostatic force. The energy released during fission is also explained by this model, as it is a result of the strong nuclear force being converted into kinetic energy.

What are the limitations of the Liquid Drop Model?

The Liquid Drop Model is a simplified model and does not take into account the quantum mechanical properties of the nucleus. It also cannot fully explain the behavior of nuclei with an odd number of nucleons, and it does not account for the shell structure of the nucleus. Therefore, while it is a useful tool, it is not a complete explanation of nuclear structure and behavior.

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