5P revision notes
Section 17.8-17.15 Nuclear Physics
Protons in nucleus repel each other electrically but attract each other by strong nuclear force.
This is very short range. Since the strong force does work on a proton to attract it, the
proton’s nuclear potential energy will fall.
The electrical potential energy of a proton a distance r away from a positive nucleus looks like
this (1/r pattern):
Nuclear potential energy looks like this:
Total potential energy looks like this:
If you have a whole lot of protons and neutrons a long way from each other, their potential
energy is zero. If you combine them together into a nucleus, their potential energy will be
negative. So you have released energy by binding them together. This is the binding energy.
The binding energy per nucleon is the binding energy divided by the total number of nucleons.
It is at a minimum for medium-mass elements such as nickel and iron. Heavier nuclei have
less binding energy per nucleon (though more binding energy altogether) because the
electrical repulsion, being long range, gets more important as the nucleus gets heavier (simple
model: every proton repels every other proton electrically, but the nuclear strong force only
attracts its nearest neighbours).
So you can release energy by splitting heavy nuclei (fission) or combining light ones (fusion).
Image from http://www.alaskajohn.com/physics/charts/binding_energy.jpg
Example:
Uranium-235 has a binding energy per nucleon of 7.591 MeV. Upon absorbing a neutron it
splits into Ba-141 (binding energy per nucleon 8.513 MeV) and Kr-92 (binding energy per
nucleon (binding energy per nucleon 8.326 MeV). Write a nuclear equation for this reaction
and work out how much energy is released.
Total binding energy of U-235 = 235 x 7.591 MeV = 1783.885 MeV
Total binding energy of Ba-141 = 141 x 8.513 MeV = 1200.333 MeV
Total binding energy of Kr-92 = 92 x 8.326 MeV = 765.992 MeV
Total binding energy of products = 1966.325 MeV
(The neutrons are not bound to anything so must have zero binding energy)
The total binding energy has gone up by 182.44 MeV (2.9 x 10-11 J) so this is the energy
released. It will be mainly in the form of kinetic energy of the fission fragments, and perhaps
some gamma rays will be emitted as well.
The products will also be less massive than the reactants by Einstein’s energy-mass
equivalence relation E= mc2. Mass change = E/c2 = 2.9 x 10-11 J / (3.0 x 108 ms-1)2 = 3.2 x 10-28kg.
This equation is universally applicable. For example, matter and antimatter annihilate to give
energy. Electron and positron (mass 9.1 x 10 -31kg each) annihilate to give gamma rays of
energy mc2 = 18.2 x 10-31 kg x (3.0 x 108 ms-1)2 = 1.64 x 10-14 J. The process can also run in
reverse, with energy being converted to particle-antiparticle pairs (e.g. in particle
accelerators).
Subatomic structure
Experiments with high energy electron scattering indicate substructure to the neutron and
proton – they are each made of 3 quarks. Up quark charge +2/3 e, down quark charge -1/3 e
(where e is 1.6 x 10-19 C). A proton is up, up, down (uud) whereas a neutron is up, down,
down (udd) for total charge zero.
Standard model: matter is made of quarks and leptons (electron, neutrino) while forces are
transmitted by bosons (photons, gluons, W&Z bosons).
(image based on one from the AAAS, displayed at
http://www.daviddarling.info/encyclopedia/S/standard_model.html)