# B Mass Defect: Is my understanding correct?

#### A M

Summary
I want to write a student article specially for those who don't have a background in nuclear physics. I've been suggested to share my basic understanding & ask if they're correct.
I would be grateful if anyone could explain where my mistakes are:
(Please note that diagrams are designed just to give a simple imagination of the article & make it more understandable; they do NOT correspond precise information.)
Mass – Energy Relationship:
According to Einstein’s special theory of relativity, when the energy of a body increases, so does its mass, and vice versa. If the difference in energy is indicated by ΔE and the difference in mass by Δm, these two quantities are related by his famous equation:
$ΔE=Δmc^2$
When 'c' is the velocity of light ($2.9979×10^8 m/s$).

Mass Defect:
The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent nucleons, this 'missing mass' is known as the mass defect. So for a nucleus (X) with Z protons and N neutrons we can write:
$m_x, m_n ,m_p$ -the masses of a nucleus (X), free neutron and free proton
$m_x<Zm_p+Nm_n$
Mass Defect= $Zm_p+Nm_n-m_x$

As it has been written in the first part, nuclear binding energy is the minimum energy we need to add to a nucleus to separate all of its nucleons.
So for the binding energy of that nucleus ($B_x$) we could write:
$m_x+B_x=Zm_p+Nm_n$
$B_x=Zm_p+Nm_n–m_x$
And we can conclude that the binding energy of a nucleus corresponds/is its mass defect [by $E=mc^2$].
Iron-56 and nickel-62 have the highest nuclear binding energy per nucleon; meaning that they have the least mass per nucleon. As a matter of fact 'more tightly bound means less massive.'

References:

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#### RPinPA

Homework Helper
Seems OK except that you're mixing units in your binding energy equations. Because $E = mc^2$ not $E = m$, there should be a factor of $c^2$ in there, unless you've explicitly stated somewhere that you're using units where $c = 1$.

• A M

#### A M

Yes you're right, but to be honest, I've already given up writing that article.
Anyway, thanks for your correction! Mentor