# Confusion over packing fraction

1. Jan 5, 2015

### fatma

so what i understand is that packing fraction is mass defect per nucleon. mass defect is the difference between total mass of the nucleons and the actual mass of the nucleus of an atom.
if A=mass number
[M][/p]=mass of proton
[M][/n]=mass of neutron
M=mass of nucleus
then packing fraction= [Z[M][/p]+(A-Z)[M][/n]-M]/A
why do some text books and websites write it as
packing fraction=(M-A)/A
where M=mass of nucleons
A=mass number
from what i have understood the numerator could not possibly mean mass defect since mass number is not equal to the total mass of nucleons.
where have i not understood well or is the problem with the text books and the websites (quite unlilkely i might say)

2. Jan 6, 2015

### Staff: Mentor

M is a mass, A is an integer, it does not make sense to subtract them. Where exactly did you see that?

3. Jan 6, 2015

### e.bar.goum

hmm. Given nuclear physicists propensity to drop units when we're feeling lazy, I wouldn't be surprised to see an equation like that. In fact, I just opened my copy of Krane, and he writes the mass defect as

$\Delta = (m-A)c^2$

Then, with all the masses in atomic mass units, you've just got to put back the implicit $c^2$ (and $c^2 = 931.50$ MeV/u). Sorry, this happens in nuclear physics an awful lot.

As it turns out, "packing fraction" is just a really archaic way of writing the nuclear binding energy per nucleon. (I learn something new every day!)