Why Does Nuclear Binding Energy Release Energy?

[sudabe]

when nucleons gather together to form a nucleus they release energy and we call it Binding energy.why is that?
we know that to keep the nucleons together they need nuclear force and exchanging the meson particles would do the job.so why a part of their mass change into energy?
I appreciate if you can help.thanks

 

[isospin]

Do you think what happens when a electron comes to a proton then they combine a Hydrogen? According to the calculation of E-M potential, The binding energy is negative, which means it costs energy to separate them again.

 

[malawi_glenn]

Just to add a thing, mass is not 'converted' into energy, E = mc^2 just implies that mass is a FORM of energy. Just as E = mv^2/2 is one form of energy (nonrelativistic kinetical).

 

[Icosahedron]

Just to add a thing, mass is not 'converted' into energy, E = mc^2 just implies that mass is a FORM of energy. Just as E = mv^2/2 is one form of energy (nonrelativistic kinetical).

Really? Why then do mass and energy have different units?

 

[malawi_glenn]

Really? Why then do mass and energy have different units?

It depends on what unit system you have :)

My point is that there is not such thing as 'pure' energy.

 

[vanesch]

so why a part of their mass change into energy?

It is not that "part of the nucleon's mass is converted to energy" ; it is that in an interacting system, the total mass of the overall system is not just the sum of the (rest) masses of the components, it is rather, the sum of the rest masses of the components minus the mass equivalent of the binding energy.

It is because we tend to think that the overall mass is the sum of the masses of the constituents, that we seem to have a "missing mass". This sum rule is a good approximation as long as binding energies have negligible mass equivalents, such as is often the case in chemistry. But it isn't generally true.

So, again, not "part of the nucleon's mass" is converted to energy. It is simply that the mass of the overall system is NOT equal to the sums of the masses of the free constituents.

 

[sudabe]

so where does the B-E come from?

 

[vanesch]

so where does the B-E come from?

From the interaction. Classical example: consider an empty space, and two clumps of mass: planet A and planet B, at billions of kilometers one from another. They are interacting through (Newtonian) gravity, and hurl one towards the other. If they don't collide, they'll separate again: we don't have a bound system. But if they collide, we'll get huge fireworks, lots of heating up, which is eventually radiated into space, and a bigger lump: a single planet, the "bound state" of planets A and B. The binding energy, is the surplus energy that was liberated during the collision, and came from the gravitational attraction that accelerated both planets onto each other. It was radiated away, mainly as radiation (heat, light, etc...). It's gone now from the system. That was the binding energy. If you want to make again planets A and B, at billions of km one from another, you will have to provide at least this binding energy to the lump we now have.

If there wouldn't have been any gravitational interaction, there wouldn't have been the acceleration, the fireworks, the radiated heat, and the final bound lump. There wouldn't have been any released binding energy.

 

[sudabe]

if they don't collide, they'll separate again: we don't have a bound system. But if they collide, we'll get huge fireworks, lots of heating up, which is eventually radiated into space, and a bigger lump: a single planet, the "bound state" of planets A and B.
thank you for your complete answer.
Can i say releasing binding energy and forming a bound system are equivalent?
I mean for example when 2 particles got the required conditions,will release energy and form bound state?
I want to have an understanding of a bound system.
(I know my questions are strange sorry:shy:)

 

[vanesch]

Can i say releasing binding energy and forming a bound system are equivalent?
I mean for example when 2 particles got the required conditions,will release energy and form bound state?
I want to have an understanding of a bound system.
(I know my questions are strange sorry:shy:)

I can't think of a counter example. I guess yes, that releasing binding energy and forming a bound system are equivalent statements...