Nuclear Reactions: Energy from Mass Difference

[FizixFreak]

Hi there in my knwoledge the energy released in any nuclear reaction is because of the fact that the mass off the reactants is greater than the mass of the products and the missing mass is converted into energy but in a nuclear reaction the bindind energy of the products is greater than that of the reactants so isn`t that missing mass being converted to the binding energies of the products and if the missing mass is converted into binding energy of the products where does the released energy come from i m quite confused about it

 

[Stonebridge]

It is confusing, but you must remember that binding energy is the energy needed to separate the nucleus into its components. (Against the attractive nuclear forces) In other words, biding energy is the energy that is released when the nucleus is formed.
So if the products have more binding energy than the reactants, that means a release of energy.

 

[vanesch]

Actually, forget about "mass being converted into energy". I know that almost all intro nuclear texts talk about that, and it is not wrong of course, but it might give the impression that in nuclear processes "something special converts mass into energy", in a different way than say, a chemical combustion. No, in nuclear reactions, just as with chemical reactions and other phenomena, constituents change their state of interaction: they change their configuration of binding. And it turns out that certain bound configurations have less energy (are more strongly bound) than others, and by conservation of energy, if you go from a loosely bound state to a strongly bound state, the remnant energy must go somewhere: kinetic energy, gamma radiation...

The ONLY fundamental difference between nuclear bound energies and chemical bound energies is their scale: nuclear bound energies are not entirely negligible wrt the rest mass of the atoms (order promille) while chemical energies are (10 orders of magnitude). And it is a consequence of special relativity that bound states are lighter than free states, so we SEE this effect with nuclear reactions, and we (almost) can't see it with chemical reactions.

 

[FizixFreak]

so basically the energy is released because of the change in binding energy but what about the mass ??

 

[vanesch]

so basically the energy is released because of the change in binding energy but what about the mass ??

Relativity says that when binding energy changes, the mass of the bound system changes (even though it has the same constituents). The thing being that in relativity, the mass of a system is NOT just the sum of the masses of the constituents, but rather the mass of the constituents minus the mass equivalent of the binding energy.

It's the same with molecules: a water molecule has a mass, slightly lower than the sum of the mass of a free oxygen atom and two free hydrogen atoms. The difference being the binding energy (in mass equivalent) of the H2O molecule versus free radicals. However, this mass equivalent is so terribly tiny as compared to the masses of the atoms, that it is almost impossible to measure (10th decimal place or something). As the binding energies in nucleae are about a million times larger, and the masses of the atoms are still the same, here you DO see this effect.

 

[Bob S]

The energy released in nuclear reactions usually includes kinetic energy of neutrons, neutrinos, electrons or positrons, and alpha particles.

Bob S

 

[FizixFreak]

so basically i can say that energy is released due to nuclear transitions ??

 

[Bob S]

so basically i can say that energy is released due to nuclear transitions ??

Yes. Nuclear isomers that emit gamma rays release energy and have less mass after the transition than before. Example: technitium 99-m (half life 6 hours)..

Bob S

 

[vanesch]

so basically i can say that energy is released due to nuclear transitions ??

Yes, exactly as with chemical (electronic) transitions. Only, the numbers are bigger.

 

[FizixFreak]

tell me one thing brother if the binding energy is increasing does that mean the nucleaons are aquiring energy or does that mean more energy is required to separate them to be honest i think that i have missunderstood binding energy

 

[FizixFreak]

dude i would really appreciate some help here
i really need to know this stuff i think the confusion was caused by misunder standing of binding energy

 

[the_house]

tell me one thing brother if the binding energy is increasing does that mean the nucleaons are aquiring energy or does that mean more energy is required to separate them to be honest i think that i have missunderstood binding energy

An increased binding energy means more energy is required to separate the nucleons. This lowers the total energy (i.e., mass) of the nucleus. If the energy of each nucleon increased, that would have the opposite effect. The total energy of the system would be larger and it would take less extra energy to separate the nucleons.

 

[curioso]

I too have found the concept of "binding energy" quite confusing, so I will share a realization which I think helped me with it.

I think confusion as to what binding energy is arises due to the definition of binding energy. By convention, positive binding energy is defined as the amount of energy required to unbind a system. Therefore, in reality "binding energy" doesn't do any binding. It unbinds. So, technically incorrect as it may be, when I am thinking of "binding energy," I think of it as "unbinding energy."

In a nuclear fusion reaction, binding energy is released and is lost from the system (the nucleus). It doesn't do any binding. It is a consequence of binding. In the reverse reaction, energy supplied from outside the system (the nucleus) overcomes the strong nuclear force and unbinds the system providing kinetic energy to the system components (nucleons).

So binding energy never does any binding. It is energy released from a fusion reaction and lost from the system or, in the reverse situation it represents energy supplied to the system which overcomes the strong nuclear force and actually leads to unbinding, not binding.

The concept of binding energy applies not only to nuclear reactions but to chemical and gravitational reactions as well and in the same manner. More tightly bound systems are rendered less massive by the loss of energy as heat or radiation. Less tighly bound systems become more massive as they gain energy.

Hope this helps. But before you buy in, we should see what others in the forum might have to say about this. They will be more qualified than me to be giving you advice.

Curioso