# What is mass defect?

## Main Question or Discussion Point

I understand that when two nuclei combine to form another nuclei . the resultant nucleon will have a lower mass than the some of the two parent nuclei. I also understand that the missing mass has been given out as energy...
Does this mean that the protons and neutrons have actually gotten "lighter"?

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Yes but the nucleus hasn't because the missing mass binds them

you can check this yourself. Take an example, like carbon 12. You have 6 protons and 6 neutrons forming the nucleus. The sum of $$6m_p + 6m_n \neq m_{C_{12}}$$

You will see that the sum of the free particle is a tad more than the mass of the nucleus. Therefore, this missing mass is turned into binding energy. Like vin300 said though, the Carbon 12 nucleus is not missing any mass.

Cheers

You will see that the sum of the free particle is a tad more than the mass of the nucleus. Cheers
That's not actually true.That's because you calculate the mass of the nucleus by adding the masses of the neutrons and protons

Yes, but tell me how do you want to form nuclei otherwise. They are formed from neucleons that bind together, through the strong nuclear interaction.

you can check this yourself. Take an example, like carbon 12. You have 6 protons and 6 neutrons forming the nucleus. The sum of $$6m_p + 6m_n \neq m_{C_{12}}$$

You will see that the sum of the free particle is a tad more than the mass of the nucleus. Therefore, this missing mass is turned into binding energy. Like vin300 said though, the Carbon 12 nucleus is not missing any mass.

Cheers
I'm a bit confused now
Doesn't the new nucleus loose energy by giving out gamma radiation? If so, shouldn't the whole nucleus be lighter?
And what do you mean by the "free particle"?

That's probably gamma decay
See the wiki page for detailshttp://en.wikipedia.org/wiki/Gamma_ray" [Broken]

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jtbell
Mentor
I understand that when two nuclei combine to form another nuclei . the resultant nucleon will have a lower mass than the some of the two parent nuclei. I also understand that the missing mass has been given out as energy...
Does this mean that the protons and neutrons have actually gotten "lighter"?
The mass defect is a property of the system i.e. the entire nucleus. You cannot associate parts of it with individual protons and neutrons. They still (individually) have the same mass as when unbound. Mass is not an "additive" property.

Hi there,

The idea was not to confuse you with some nuclear theory. But, I'll try to give you a few details more.

Nuclei are made of nucleos (protons and neutrons) that are bound together through the strong nuclear interaction. These nucleons' distribution is not always the same (like for the electrons around a nucleus). Therefore, and stochastically, nuclei will disintegrate through three different possible process: alpha decay, beta decay, and spontaneous fission. The alpha decay is simply the emission of an helium nucleus. The beta decay is the emission or absorption of electrion/positron. And spontaneous fission is the nucleus breaking in two part.

Very often, when "playing" with the nucleus, the nucleons can be left in an excited state. After a certain time, the nucleons will rearrange into a more favorable energy state, emitting gamma radiation.

Hope this helps, without going too much in details.

Cheers

Thanks fatra2
I understood that post pretty well ;-)..
Since you started from the beginning, I continue from where you left of..
My first question:
So what is the mass defect?
The previous posts tell me that the neucleons do not get lighter but, as I understand the nucleus as a whole looses some mass.. right?

My second question:
Is this mass converted to energy and lost as gamma radiation or is it turned into something called binding energy?
(my text book says that the nucleus emits the gamma rays and thus, as it looses energy it becomes more stable. Therefore, the energy emitted is called the binding energy... atleast that's what i understood.)

The mass defect is a property of the system i.e. the entire nucleus. You cannot associate parts of it with individual protons and neutrons. They still (individually) have the same mass as when unbound. Mass is not an "additive" property.
So if the protons and neutrons have the same mass, then what looses mass? i.e "what becomes lighter?"

My second question:
Is this mass converted to energy and lost as gamma radiation or is it turned into something called binding energy?
(my text book says that the nucleus emits the gamma rays and thus, as it looses energy it becomes more stable. Therefore, the energy emitted is called the binding energy... atleast that's what i understood.)
When the nucleons bind together to form a nucleus, they are in a state with lower potential energy than unbound nucleons. The "binding energy" is how much energy you have to put back in to break the system apart again, and is equal to the potential energy difference between the bound system and a bunch of non-interacting nucleons.

Generally the energy "lost" from binding the particles together leaves the system as gamma rays.

So if the protons and neutrons have the same mass, then what looses mass? i.e "what becomes lighter?"
The nucleus as a whole becomes lighter, the individual particles do not. (The potential energy of the system is a property of the system as a whole, not individual components--If you separate a deuterium nucleus into a proton and a neutron, it makes no difference whether you're moving the proton away from the neutron or vice-versa)

$$m_{nucleus}+ {E_{binding} \over c^{2}}= \sum m_{particles}$$

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Generally the energy "lost" from binding the particles together leaves the system as gamma rays.

The nucleus as a whole becomes lighter, the individual particles do not. (The potential energy of the system is a property of the system as a whole, not individual components--If you separate a deuterium nucleus into a proton and a neutron, it makes no difference whether you're moving the proton away from the neutron or vice-versa)

$$m_{nucleus}+ {E_{binding} \over c^{2}}= \sum m_{particles}$$
That's where I have my problem.
The nucleus is made up only of protons and neutrons. So if neither the protons or the neutrons loose mass, then how can the nucleus become lighter?

The nucleus is made up only of protons and neutrons.
That's where you have a problem.The binding energy, as Phaseshifter wrote, contributes to the mass of the nucleus by E/c^2. Writing the mass of the nucleus as mass of protons and neutrons confuses

but on the other hand..
as I stated in my previous post and as far as I understand, binding energy does not exist in the nucleus. It is more or less a hypothetical amount of energy which can be though of as a stabilizer of the atom. (but in reality it takes the form of energy emitted as radiation). (pls correct me if i'm wrong here)
If that's the case binding energy cannont contribute to the mass of the atom can it?

It is more or less a hypothetical amount of energy which can be though of as a stabilizer of the atom.
What?Hypothetical? Hypothetical energy comes out of an atomic bomb?

well.. no... not when you put it like that. :-) ;-)
but...
binding energy is described as the amount of energy that was ejected out of the atom when the nucleons joined to form the nucleus. The same energy has to be put in to the atom to break it up and hence it is though of as "holding (or binding) the nucleons together. So it seems to me that the energy we call binding energy is ... the lack of energy within the nucleons. (and hence increased stability)
again.. that's my understanding of it.
So I'm wondering how binding energy can contribute to the mass of the nucleus.

O o I was wrong in that it contributes to the mass of the nucleus.
The nucleus doesn't become lighter.Only that part of the work to be done to bring the nucleons together into a nuclide is given out as the binding energy.

Could you please explain that a bit more?

Here's a summary of my initial question after the info I've gathered from these posts.

When nucleons come together to form a nucleus they release energy. This release in energy makes the atom more stable and ,hence, is called binding energy. However, the protons and neutrons do not get "lighter".
So what is converted into energy?

You don't need to worry about information until there is wikipediahttp://en.wikipedia.org/wiki/Binding_energy" [Broken]

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How can you people be so confused?

You can't even figure out if the byproducts of a nuclear reaction weight less than the reactants which created the nuclear reaction? You don't know the facts? Why do you think that Einstein is famous for the equation E=mc^2?

The concept of binding energy applies for both nuclear and chemical reactions. However, mass defect is only believed to exist for nuclear reactions.

Also, according to General Relativity, the gravitational mass is the same as inertial mass. It is fair to say that is the type of mass we ought to consider as "mass".

Gravity, according to General Relativity, is determined by the stress-energy tensor. The stress-energy tensor not only includes mass but also light as well as all forms of energy.

The gravitational mass for matter falls as it emits energy exothermically (as long as it is a nuclear reaction). That is straight from General Relativity. Chemists don't like to hear that the mass of chemicals fall as a result of an exothermic reaction. In any case, the small difference is practically unverifiable, so it is assumed, as a practical matter, that exothermic chemical reactions don't convert mass into energy. I don't see any chemists claiming otherwise.

The concept of binding energy applies for both nuclear and chemical reactions. However, mass defect is only believed to exist for nuclear reactions.
Actually it would be more correct to say the mass defect is only currently detectable for nuclear reactions. The binding energies in chemical bonds are a million times smaller than the binding energies in nuclei, so one would expect a proprtionally smaller mass defect. We currently don't have mass measurements precise enough to detect whether that actually is the case or not.

The mass of a charged particle must include its mass energy in the electrostatic field and this amounts to some of mass of the nucleus equivalent to pot en of the system.

How can you people be so confused?
You certain aren't helping with posts like this.

vin300.. does that mean that some of the charge is lost?

vin300.. does that mean that some of the charge is lost?
Charge is only lost in disintegration of heavy nuclei.The binding energy here is not enough to bind all nucleons
In the original case, a major amount of the work to bring them together is lost as binding energy and the remaining contributes to slight increase in potential energy, an equivalent mass is gained, but almost negligible, so people don't talk about it
In heavy nuclei, the potential energy is more, it uses this energy to push out some

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