# Nuclear binding energy and mass difference

1. Sep 2, 2016

### Hercuflea

1. The problem statement, all variables and given/known data
The textbook on nuclear physics I am going through says:

"The atomic weight M of a nuclide of mass number A can be found in the mass difference, $\Delta$, given in column 3. The quantity $\Delta = M-A$ gives the difference between the nuclides atomic weight and its atomic mass number, expressed in MeV."

2. Relevant equations

$\Delta = M-A$

3. The attempt at a solution

My question is if the mass difference is defined to be the mass of a particle minus the sum of the masses of the particle's parts, why does a free neutron have a mass difference of $\Delta = 8.0714 MeV$ instead of $\Delta = 0 MeV$?

Also, if the atomic weight of Carbon, (from the periodic table) is 12.011 amu and it's atomic mass A=12, then why is $\Delta =M - A = 0$ for Carbon?

2. Sep 2, 2016

### drvrm

The nucleons in a stable nucleus are held tightly together.

Therefore, energy is required to separate a stable nucleus into its constituent protons and neutrons.

The more stable the nucleus is, the greater is the amount of energy needed to break it apart. The required energy is called the binding energy of the nucleus.
The atomic mass unit is defined as 1/12 of the mass of an atom of carbon. In terms of this unit, the mass of a carbon atom is exactly 12 u.
If one adds up the nucleon's masses in atomic mass unit (u) one will get a mass defect and its equivalent energy is binding energy of carbon.

3. Sep 2, 2016

### Hercuflea

Why does the book say the mass difference is atomic weight minus atomic mass? Wouldn't that be 12.011 - 12 = 0.011 amu?

4. Sep 2, 2016

### drvrm

I think there is error in terminology being used- In popular nuclear physics atomic weights are being used(it may include the mass of electrons)
Carbon -12 is a nuclide (a group of protons and neutrons) these protons/neutrons are not having mass as equal to one atomic mass unit
A proton has mass = 1,0073 u ,similarly a neutron has mass= 1.0087 u so adding up together these twelve nucleons will have larger mass and the
mass defect converted to energy units will give its binding energy say about 7.5 MeV per nucleon as 1 u= 931.5 MeV
in the above about .008 u is average difference per nucleon so converted to energy it will approx. to about 7.5 MeV

one can see detail calculations in <http://staff.orecity.k12.or.us/les.sitton/Nuclear/313.htm> [Broken] for model calculations on say He nucleus etc.

Last edited by a moderator: May 8, 2017
5. Sep 2, 2016

### Hercuflea

I still dont really understand why the mass defect of a single neutron should be 8.0714 MeV?

6. Sep 2, 2016

### Hercuflea

In other words, my question is basically about what the textbook means when it says
$$\Delta = M - A$$

It seems to be subtracting a unitless number A from a number M with units of either $\frac{MeV}{c^2}$ or $u$? The table in the back provides $\Delta$ values in $MeV$, not $\frac{MeV}{c^2}$. How is he getting units of $MeV$ by subtracting $\frac{MeV}{c^2} - (unitless~integer)$?