Some particles are stable, others are unstable. The most important
rule here is conservation of energy. In any reaction the final
energy must be exactly equal to the initial energy. A particle of a
given mass has a certain amount of energy, given precisely by
Einstein’s equation E = mc2. In asking if a particle can decay,
one must first try to find a set of particles whose total mass is
less than that of the particle under consideration. A particle with
a mass of 100 MeV cannot decay into two particles with a total
mass exceeding 100 MeV. The law of conservation of energy
forbids this, and Nature is very strict about this law. For more
massive particles there will usually be enough energy available,
and therefore they tend to be unstable. Excess energy is carried
away in the form of kinetic energies of the decay products.
Let us turn once more to neutron decay. The neutron has a
mass of 939.57 MeV and it decays into a proton, an electron and
an antineutrino:
neutron -> proton + electron + antineutrino
The proton has a mass of 938.27 MeV, the electron 0.511 MeV
and the antineutrino mass is very small or zero. One sees that the
sum of the masses of the electron and the proton is 938.78 MeV,
which is 0.79 MeV less than the neutron mass. From an energy
point of view the decay can go, and the excess energy is carried
off in the form of kinetic energy of the proton, electron and
antineutrino.
However, the energy balance is not the whole story. Why for
example is there an antineutrino in this reaction? And why is
the proton stable? It could, energy wise, decay into an electron and
a neutrino, to name one possibility. Here enters an important
concept, namely conservation of electric charge. Charge is always
strictly conserved. Since the proton has a charge opposite to that of
the electron, that decay, if it were to occur, would have a different
charge in the initial state (the proton) as compared with the final
state (an electron and an electrically neutral neutrino). Thus there
may be conservation laws other than conservation of energy that
forbid certain reactions. The law of conservation of charge was
already a basic law of electromagnetism even before elementary
particles were observed. There are several conservation laws on the
level of elementary particles, and some of them remain verifiable
macroscopically. Charge and energy are the foremost examples.
On the elementary particle level electric charge has a very
special feature: it occurs only in discrete quantities. Measuring the
charge in units in which the charge of the electron is - 1, one
observes charges which are integers, or for quarks multiples of 1/3.
In other words, charge is quantized. This allows us to formulate
this conservation law slightly differently; the charge appears as a
number, and counting the charge of any configuration amounts
to adding the numbers of the various particles. Let us call that
the charge number. Conservation of electric charge means that the
charge number of the initial state must be equal to that of the
final state. For example, for neutron decay (neutron -> proton
+ electron + antineutrino) the charge number of the initial state
is zero, while for the outgoing state it is + 1 (proton) plus - 1
(electron) which gives zero as well. We may speak of charge as a
quantum number. The charge quantum number is conserved.
This then is our first example of a quantum number: the electric
charge of a particle.
|
Disclaimer
