# Liquid Drop Model of the Nucleus

• venomxx
In summary, Cu-64 can decay by beta- or beta+ decay, depending on the energy gap between the parent and daughter nuclei.

#### venomxx

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?

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 alot!