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Some nuclear physics questions
By Andrew Smith (P2517) on Tuesday, June 20, 2000 - 10:35 pm:

This is quite hard to explain so please bear with me. As I understand things, if an atom has too many neutrons then it is unstable and decays (because the strong nuclear force is overcome by the excess mass?) and if it has too few neutrons then it also decays. When I talk about too many or too few neutrons I mean compared to its stable form, i.e. carbon12. The reason we've been given at school for the too few neutron part is that the atom "wants to be more stable" but I don't really see why. Can someone please explain why atoms with too few or too many neutrons decay?

Also chlorine35 and chlorine 37 are both stable so I would think that chlorine 36 would be very stable but is in fact an unstable isotope, why is this?

Also why do electrons not fall into the nucleus as they have opposite charges and so should attract? Circular motion seems to be used to explain this, using classical mechanics, but with changes in electron energy levels they should stop doing circular motion and fly about. Does this need quantum mechanics to explain it? What is the best explanation?

By Sean Hartnoll (Sah40) on Wednesday, June 21, 2000 - 12:12 am:

I'm afraid I can't answer the nuclear physics questions - and I've just finished my third year at uni!
I suspect, well in fact I am sure, that a proper explanation would require quantum chromodynamics (which I might do some of next year). Any other explanation you get is going to be fudged somewhere, but perhaps someone knows a decent A-level standard explanation?

I can be more helpful about the electrons though. The stages in the though process are as follows:

i) a priori one might think that there is no problems with orbiting electrons, after all planets don't fall into the sun and can change there orbits if they get hit by meteorites or something (analogous to photons hitting the atom say). However...

ii) it turns out that the analogy with gravity doesn't hold because in electromagnetism you also have a magnetic field that is related to the electric field, through Maxwell's equations. When you do a proper (nontrivial) relativistic calculation you find that accelerating charges emit radiation, and so lose energy. So in fact the electron would fall into the nucleus under classical physics. This was a conceptual motivation for quantum mechanics...

iii) So the problem does need quantum mechanics. In QM the electron (take one for simplicity) is described by a wavefunction, giving the probablilty of finding the electron at each point in space. One can look for particular wavefunctions which are independent of time, these exist and are called stationary wavefunctions. The energy levels in the atom correpsond to stationary wvefunctions. We say the electron is "in" an energy level if its wavefunction is the corresponding wavefunction to that energy level. The problem of falling into the nucleus doesn't arise. Or rather, it is resolved by the fact that there are stationary wavefuntions describing electrons in atoms (the stationary wavefunctions are solutions to the differential equation called Schrodinger's equation, so if you like the reason they don't fall in is because for the case of an atom this equation has a solution, although only for certain values of energy, which is where, in fact the energy levels come from in the first place, as opposed to have a continuum of energy levels).

Hope this helps,

Sean