# Defect mass and Binding energy

We know that the Einstein formula $E=mc^2$. In reaction we use this formula to calculate binding energy of that reaction. We use $E_{\text{binding}}=\Delta mc^2$, where Here $\Delta m$ is defect mass.

We also know that binding energy can not be negative and by the formula of binding energy in terms of $\Delta m$, it can be postie and negative also just because $\Delta m$ can be negative.

• see hyperphysics.phy-astr.gsu.edu/hbase/NucEne/nucbin.html . please note that the $Δ(m)$ used in nuclear physics is the invariant mass one, not the einstein relativistic mass. It is the length of the four vector , $(E,px,py,pz)$ .Protons and neutrons have a fixed invariant mass when free, When bound in a nucleus the mass of the nucleus is less than the sum of the masses of the nucleons it contains, which gives the binding energy. May 26, 2018 at 17:58

I think that you have confused the binding energy of a nucleus with the Q-value of a nuclear reaction both of which are found using the relationship $E=\Delta m \, c^2$.

The mass defect of a nucleus is equal to the sum of the individual masses of all the particles which make up the nucleus minus the mass of the whole nucleus and it is a positive quantity.

Multiplying the mass defect by the speed of light squared gives you the binding energy of a nucleus - the energy required to split up a nucleus into its constituent parts.

In reaction we use this formula to calculate binding energy of that reaction.

If there is a reaction of the form $A+B \rightarrow C+D$ then the change in mass is

$(m_A+m_B) - (m_C+m_D)$

and the Q-value of the reaction is given by the equation

$Q=[ (m_A+m_B) - (m_C+m_D)] \, c^2$.

In such an example the value of $\Delta m$ and hence $Q$ can be either positive or negative and you will often see the equation for the reaction written as $A+B \rightarrow C+D+Q$.

Usually the binding energy is take positive so that $E = E_1+E_2-B.E.$ for a system considering of two parts bound together. By the way if $\Delta m >0$ then the system will fall apart.