Non-scientist's query regarding nuclear fusion

[AJH]

Encyclopedias and the like seem to explain the energy gain from nuclear fusion reactions (as in the sun) in the following manner: for elements with atomic weights less than iron, the HIGHER the weight of the atom the less binding energy needed to overcome electromagnetic repulsion in the nucleus -therefore two hydrogen atoms fusing into one helium will release an excess of the binding energy. I have two questions:

1) This binding energy (which I'm assuming is equivalent to the srong nuclear force) - why would hydrogen atoms have any when they only have the on eproton in their nucleus and there can be no like-on-like repulsion?

2) How does the excess of binding energy lead to electromagnetic radiation?

I would be grateful for any advice.

 

[daveb]

1. If I understand your question correctly, you wonder why hydrogen (H-1) can have a binding energy with only a single proton? Nuclear binding energy arises from the attraction of the Strong nuclear force between nucleons (protons and neutrons). In a nucleus, this binding energy is stronger than the electromagnetic repulsion force that would exist if the nucleus contained more than 1 proton. The more nucleons, the stronger the total strong force is in the nucleus. However, as nucleons are added, the size of the nucleus gets bigger, so the ones near the outside of the nucleus are not as tightly bound as the ones near the middle of the nucleus. The binding energy per nucleon, because of the variation of the strong force with the distance, increases until the nucleus gets too big and the binding energy per nucleon starts decreasing again. This binding energy per nucleon achieves a maximum around A = 56, and the only stable isotope with that A number is iron-56. So the way fusion works in a star is that the force of gravity is strong enough to get the nucleons close enough together so that the EM repulsion is overcome, causing fusion. So, looking at hydrogen, once its nucleus gets close enough to fuse with more nucleons (say in another hydrogen) energy is released.

2. Think of excess binding energy like a ball on a staircase, where the ground state (the state where the ball has the least energy) is the ball at the bottom of the stairs. If the ball is somewhere on one of the steps, at some point the ball rolls down the stairs. The potential energy of the ball at the higher step is released as sound energy (assuming no other mechanism for energy release existed). In a nucleus, the excited states of the nucleus are the steps of the staircase, and the gamma photon that is released from the nucleus is analagous to the sound energy that is released.

 

[AJH]

Still struggling with hydrogen-to-helium fusion

Ah, so the binding force in a hydrogen atom is between the proton and neutron. Thanks also for the staircase analogy. However...

The more nucleons, the stronger the total strong force is in the nucleus. However, as nucleons are added, the size of the nucleus gets bigger, so the ones near the outside of the nucleus are not as tightly bound as the ones near the middle of the nucleus. The binding energy per nucleon, because of the variation of the strong force with the distance, increases until the nucleus gets too big and the binding energy per nucleon starts decreasing again.

If the binding energy per nucleon INCREASES in atoms as atomic weight increases (up until lead) how can there be a binding energy surplus when hydrogen atoms fuse to form the heavier helium atom - surely there would be a binding energy defecit.

I must be getting confused as different sources seem to disagree as to whether the binding force per nucleon increases or decreases with atomic weight.

 

[cesiumfrog]

Uh, firstly, hydrogen normally does not contain any neutron (just the one nucleon, a proton).

The most "stable" atom is of Iron. This is to say, the lowest energy state for a collection of nucleons is a state in which they are grouped into iron nuclei.

If you try to concentrate a larger number of nucleons into the nucleus, the basic problem (simplified, no doubt) is that the (long range) electrostatic repulsions between the protons will be more strained, increasing the amount of potential energy stored (on a per-nucleon basis). As nuclei gets larger, you can imagine it stretching further than the strings of "glue" holding it together (the short range "strong force") can reach. So, with heavy atoms (like Uranium), you will release a lot of electrostatic energy if you let the atom split in two (and this won't be prevented by the strong force, which hardly reaches across such large nuclei).

But if you try to break Iron nuclei in two, even though the electrostatic repulsion will help you, you'll need to provide even more energy. This is because the nucleus is small enough for the strong force to "hold both ends together", you need extra energy to overcome this force. Conversely, if you take two little deuterium nuclei, and hold them near together (by supplying a little bit of energy to get past the long range electrostatic repulsion, and bring them just into range of the strong force) then they'll tug so tightly toward each other that you can obtain lots of energy letting them fuse the rest of the way together.

It seems like you're confused by thinking to much of "binding energy" as something "contained" in atoms.

 

[AJH]

Thanks for the reply, 'frog. OK, I can deduce there can be no binding energy in a simple hydrogen atom. I had read about iron being the most stable atom (don't know where I got lead from in the previous post...)

You're right, I was preoccupied with the notion of binding energy being somehow "in" the nucleus as opposed to being mediated separately and I think I've got it now thanks to Dave B's staircase analogy regarding stability and potential energy.

Always nice to have your queries resolved!

 

[Astronuc]

A tutorial on binding energy - http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html

Fusion - http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html#c4 (same page)

Proton-proton chain for stellar fusion - http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html

CNO cycle - http://csep10.phys.utk.edu/astr162/lect/energy/cno.html

http://csep10.phys.utk.edu/astr162/lect/energy/cno-pp.html

Stellar plasmas, where the fusion takes place, have much higher particle (ion/electron) densities than can be created on Earth because we cannot develop sufficiently strong magnetic fields and magnets. In addition to particle density, fusion requires high temperatures (millions of K) to proceed.

 

[malawi_glenn]

Ni -56 has the largest binding energy per nucleon, not Iron, right?

 

[Astronuc]

http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin2.html

One might wish to review

Wapstra, A. H. and Bos, K., "The 1983 atomic-mass evaluation. I. Atomic mass table," Nucl. Phys. A 432, 1-54, 1985.

 

[malawi_glenn]

Ni 62, sweet :)