both position and momentum, the Heisenberg uncertainty principle limits the accuracy with
which one can know it. The most that can be known about an angular momentum vector is its
magnitude and one of its three vector components, both of which are quantized in units of~.
In addition to the angular momentum that an electron carries by virtue of its motion through
space, it possesses an intrinsic angular momentum with a magnitude of~/2. Protons and
neutrons also have spins of~/2, while the photon has a spin equal to~.
Particles with half-integer spin obey the Pauli exclusion principle: only one such particle
can exist is a given state, i.e., with a given combination of quantum numbers.
We can enumerate the lowest-energy states of hydrogen as follows:
n= 1, = 0,z= 0, sz= +1/2 or− 1 / 2 two states
n= 2, = 0,z= 0, sz= +1/2 or− 1 / 2 two states
n= 2, = 1,z=−1, 0, or 1, sz= +1/2 or− 1 / 2 six states
......
The periodic table can be understood in terms of the filling of these states. The nonreactive
noble gases are those atoms in which the electrons are exactly sufficient to fill all the states up to
a givennvalue. The most reactive elements are those with one more electron than a noble gas
element, which can release a great deal of energy by giving away their high-energy electron, and
those with one electron fewer than a noble gas, which release energy by accepting an electron.