Question on Nuclear Energy: Why Does a Nuclei Weigh Less?

[Clausius2]

When I took my nuclear energy course, I came up with a doubt that has remained active till today. I've search in physics books for it, but I've not found any consistent explanation.

The question is why a nuclei of some element weigh less than the sum of the masses of their components?.

I mean, a proton in a nucleus seems to weigh less than other out of it.

If I'm wrong with that, please let me know it. Maybe I don't remember well.

 

[marlon]

This is because the binding-energy hollding the nucleus together is also accounted for as mass. remember thay E=mc² so the binding energy corresponds to a mass equal to E/c²


regards
marlon

 

[marlon]

Besides Clausius2, not some elements...like in your question. This fact shall always be the case...

regards
marlon

 

[humanino]

Nop. Physics never answers why. It answers how.

 

[Clausius2]

Thanks for your reply, Marlon. I know you are some like an expert in these business.

Ok. I must said any element.


I thought about the binding energy as you said. It seems like binding energy takes away a bit of mass in order to mantain nulei united. Although I was waiting for a similar answer, you have not answered my question. I know a lot of energy process that seems not to feed themselves with the surrounding mass.

Why does the binding energy need mass to enhance nuclei union?.

Maybe I'm telling you a misconception, but I think other energies, like the magnetic energy that holds two magnets united does not take mass of any of the magnets, doesn't it?. Maybe you could say the electromagnetic force is enhanced due to photon exchange...

Do you understand me?

Now you're going to answer me with Einstein equation: E=mc2...

I'm a bit confused...Perhaps the appropiate question would be how the binding energy acts. I mean, how proton and neutron are united, which is the mechanism of the force exerted, and why it takes some mass of the two particles.

 

[Clausius2]

Thanks for your reply Humanino, but I have the opinion that sometimes physics laws are able to answer "why?" questions, except you keep on questioning "why?" till you reach the universe creation instant...
Be sure I'm not going to do that.

 

[marlon]

Protons and neutrons are baryons that constist out of three quarks. These quarks are bound together by the strong force mediated by the gluons. If you add up the three masses of the quarks you do not get the mass of the baryon. There will be an extra mass-term that has to be included due to the energy that holds the three quarks together. Einstein said that mass and energy are equivalent. This means that wherever there is a mass m , you can also speak of an energy equal to E/c². This does NOT mean that the mass is converted into this energy, so NO MASS IS TAKEN AWAY and then converted into the energy.

The baryons in the nucleus of an atom are bound together by the strong force also. Yet one big difference : the strong force (more specifically the residual strong force) is mediated by pions (the lightest mesons or quark-antiquark-pair) and not by gluons like in the baryons themselves.


hasta la vista
marlon

 

[marlon]

Maybe you could say the electromagnetic force is enhanced due to photon exchange...

that is very true,

the EM-interactions are mediated by the photons
the strong force is mediated by the gluons
the residual strong force is mediated by the pions
the weak-interaction is mediated by the vector-bosons
the gravitational-interaction is mediated by the "graviton", well this is under construction.

One remark : the pions are the only particle in this list that is not FUNDAMENTAL and elementary...

regards
marlon

 

[humanino]

Take the system Earth-Moon and weight it. Note the result.
Now tear them apart, and weight each of them separately : amazing, the sum of the masses is larger than the mass of the initial system.

 

[humanino]

Hey Marlon !

If you add up the three masses of the quarks you do not get the mass of the baryon.

You know how fascinated I am by hadrons. Yet this is such a peculiar and unique situation in Nature : the masses of the quarks is totally negligible compared to the binding energy, or mass of the hadron.

 

[marlon]

Hey Marlon !

You know how fascinated I am by hadrons. Yet this is such a peculiar and unique situation in Nature : the masses of the quarks is totally negligible compared to the binding energy, or mass of the hadron.

Right on Humanino, you are correct.

i was just setting the example, you know...

regards
marlon

 

[humanino]

Yes I know. I'm a pain in the ... you know. You should get an award for helping people. I should get a warning for constantly making counterpoints and playing "the devil's advocate".

 

[Clausius2]

This does NOT mean that the mass is converted into this energy, so NO MASS IS TAKEN AWAY and then converted into the energy.

Take the system Earth-Moon and weight it. Note the result.
Now tear them apart, and weight each of them separately : amazing, the sum of the masses is larger than the mass of the initial system.

Ok. I think I have a deep problem. First of all, what do you mean with "to weigh"?. What is the meaning of weight of Earth-Moon system?. Do you mean I stop the rotating movement with my exclusive strenght , and then I weigh the two bodies. They'll weigh the same. How can I measure the weight of something that is in movement?. I can only imagine that in its reference frame where v=0. By contrast, are you saying the gravity force makes two bodies to weigh less?

Marlon, if you have a nuclei at rest in front of you, that nuclei weigh less than the sum of their components. For the same reason, I weigh less now I'm on Earth than when I go for a walk into the inter-planetary space where gravity force is less intense?. If so, where is this defect of mass? Who has stolen part of my mass ?

Au revoir .

 

[marlon]

Yes I know. I'm a pain in the ... you know. You should get an award for helping people. I should get a warning for constantly making counterpoints and playing "the devil's advocate".

No man, I like you,

I think we should both get an award. You knew we were nominated ? Just check out the "more democratic process in awarding medals"-thread...

Devil's advocate ?

I want to be Al Pacino, you are Keanu Reeves ?

Who are you carrying all these bricks for anyway ?? God is that it?

regards
marlon

 

[marlon]

Clausius, the nucleus has smaller mass because of the negative potential energy that is associated with it in that case. This is not always true though...

For Coulomb interaction the potential energy is negative, thus the term E/c² is negative and thereby the massvalue is reduced a little bita. You get mass of particle 1 + mass of particle 2 - mass due to binding-energy.

Also remeber that the difference between the different types of energy (binding-, kinetc- ,potential-energy) coming from classical mechanics, is not adopted into SR and GTR. They are all just energy...


regards
marlon

 

[humanino]

First of all, what do you mean with "to weigh"?. What is the meaning of weight of Earth-Moon system?. Do you mean I stop the rotating movement with my exclusive strenght , and then I weigh the two bodies. They'll weigh the same. How can I measure the weight of something that is in movement?. I can only imagine that in its reference frame where v=0. By contrast, are you saying the gravity force makes two bodies to weigh less?

Of course, I only wanted to illustrate binding energy as universal, and when one includes Einstein's $$E=m$$... But then, I don't know how you could actually weight this system.

Marlon : nominated
I don't want no award ! PF would be discredited by my posts.

 

[Clausius2]

I'm a pain in the ... you know. You should get an award for helping people.

No man, I like you,

uhh.. here is a some like a love story between you...

Maybe you should go together and have a romantic dinner...

Sorry, I was joking.

France-Belgium, what a pretty friendship...

 

[humanino]

We will have a romatic dinner someday for sure. I am too far right now

 

[marlon]

We could have a threesome, ok?

A romatic dinner in Spain with a nice French wine, some paella and some Belgium sweet-chocolates as dessert

Viva l'amour international, aiaiaiiiiiiiiiii

 

[humanino]

Are you gay too Marlon

 

[marlon]

mmmmmmmmmmmmmmmmmmmmmmmm

 

[da_willem]

Marlon, if you have a nuclei at rest in front of you, that nuclei weigh less than the sum of their components. For the same reason, I weigh less now I'm on Earth than when I go for a walk into the inter-planetary space where gravity force is less intense?. If so, where is this defect of mass? Who has stolen part of my mass ?

You confuse mass with weight. Weight is the force acting on a body in a gravitational field. So is proportional to the mass, but depends on the gravitational field as well. The mass is (almost) constant in this example. So this is something very different from an interacting system weighing less than it's components.

 

[Clausius2]

Then, how would you measure the mass of a nuclei?. And how would you measure experimentally the mass of a proton?

 

[marlon]

The mass of charged particles can be measured using mass-spectrography.

In order to measure the mass of nuclei you also need to have an idea on how strong the constituent particles that make up the nucleus are bound.

Ofcourse this is difficult to determin so this is not done in practice...

regards
marlon

 

[aww0110]

Hello,

I am fairly new to the forum, but my professor has asked this question as part of his assigned homework for this week, and I am at wit's end on trying to solve it.

I understand how for small particles this phenomena could occur, but for the Earth - Moon system, how does one go about measuring the binding energy between the Earth and the moon, and thus calculating the mass deficit of that system?

I know that in theory:
Energy of the system = Energy of the parts - E binding
Energy of the system at rest = mass system * c^2
Mass deficit = Energy of binding / c^2

I thought perhaps the energy of binding would be related to the gravitational pull between the Earth and the Moon, or the centripetal force required to keep the moon in orbit around the Earth. But for these quantities to even get the correct units, I would have to multiply by a distance (what distance?). SOmething about this just seems nonsensical, because I calculate the centripetal force using the moon's original (freestanding mass) and the gravitational pull using both object's freestanding masses.

Help?

 

[malawi_glenn]

http://www.iop.org/EJ/article/0031-9120/25/6/307/pev25i6p322.pdf?request-id=59786322-48d5-4db8-938c-0f51b950a460

 

[Gokul43201]

I thought perhaps the energy of binding would be related to the gravitational pull between the Earth and the Moon, or the centripetal force required to keep the moon in orbit around the Earth.

Yes, it is. But the quantity you want is the gravitation potential energy of the two-body system.

 

[aww0110]

I kind of get this problem now.

I think I should include both the potential energy of the moon and the kinetic energy of the moon to find out the binding energy between the moon and the earth. More binding energy is required because the moon is in motion around the Earth than if the moon was sitting at a certain radius from the earth.