# Confusion over packing fraction

• fatma
In summary, the conversation discusses the concept of packing fraction in relation to mass defect and the mass of nucleons in an atom. It is explained that some textbooks and websites write the equation for packing fraction as (M-A)/A, which seems incorrect based on the understanding that mass defect is the difference between the total mass of nucleons and the actual mass of the nucleus. However, it is noted that this could be due to the tendency of nuclear physicists to drop units in equations. Overall, it is concluded that packing fraction is essentially the nuclear binding energy per nucleon.

#### 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 textbooks 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 textbooks and the websites (quite unlilkely i might say)

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

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

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!)

## 1. What is the definition of packing fraction?

Packing fraction is a measure of the efficiency of how particles are packed together in a given space. It is the ratio of the volume occupied by the particles to the total volume of the container.

## 2. How is packing fraction calculated?

Packing fraction is calculated by dividing the volume of the particles by the total volume of the container and multiplying by 100 to get a percentage.

## 3. Does packing fraction affect the properties of a material?

Yes, packing fraction can affect the properties of a material. Materials with a higher packing fraction tend to be more dense and have stronger intermolecular forces, while materials with a lower packing fraction may be more porous and have weaker intermolecular forces.

## 4. Why is there confusion over packing fraction?

There can be confusion over packing fraction because the term is used in different contexts and can have different meanings. It can also be calculated in various ways, leading to different results.

## 5. How can packing fraction be used in real-world applications?

Packing fraction is important in many fields, such as materials science, chemistry, and biology. It can be used to understand the structure and properties of materials, optimize packing processes in manufacturing, and predict the behavior of particles in different environments.