How Does Binding Energy Affect Mass in Nuclear Reactions?

[DiamondV]

Homework Statement

We just started binding energy things in class starting off with e=mc^2 and well in my notes it says. "If weakly bound nuclei transform into more strongly bound nuclei, the total mass can be reduced and the mass energy of the final state is lower than the mass energy of the initial state

Homework Equations

The Attempt at a Solution

Heres how I understand that sentance.
In the initial state the nucleons inside the weakly bound nuclei are bound weakly to each other, this means that there is low binding energy between them.
In the final state the nucleons inside the strongly bound nuclei and strongly bound to each other, meaning that there is a high binding energy between them.
What I don't understand is how the "total mass can be reduced".
Also it goes on to say "and the mass energy of the final state is lower than the mass energy of the initial state"
If the binding energy is higher in the final state, surely the energy in the final state is higher? I mean unless the mass change overides that or has a greater impact than the energy change. Thats how I see it.

 

[xXhumans0monstersXx]

I did some research online and found a statement that said that energy, which was represented by Q = -Δm(c^2), is equivalent to mass. So I'm guess that's why the mass can be reduced, because the total energy was less. Forgive me if I'm wrong, I'm taking AP Physics 1 which doesn't really cover binding energy.

 

[ehild]

Read:
https://en.wikipedia.org/wiki/Nuclear_binding_energy

Nuclear binding energy

is the energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleons. The binding energy of nuclei is due to the attractive forces that hold these nucleons together and this is usually a positive number, since most nuclei would require the expenditure of energy to separate them into individual protons and neutrons. The mass of an atomic nucleus is usually less than the sum of the individual masses of the constituent protons and neutrons (according to Einstein's equation E=mc2) and this 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.[/qoute]

So the nucleus is at a lower energy with respect to the energy of the free nuclei. Taking that energy zero, the energy of the nucleus is negative, just as its mass is less than the sum of masses of the constituents.

The energy of a bounded system is lower than the energy of the free constituents. Think of a planet and the Sun. The planet orbiting around the Sun has negative energy.