stekas@hou2g.UUCP (J.STEKAS) (02/11/84)
Everyone knows that Fermions obey Pauli statistics - i.e. no two
Fermions can be in the same state at the same time. That is why
atomic orbitals become filled when 2 electrons (of opposite spin)
occupy them.
Now, when an atom is in a magnetic field the spectral lines get split
due to the Zeeman effect. So what used to be identical electron states
(except for spin) are now correspond to entirely different energy levels.
Question - since the electrons in these new states now have no Pauli
partners, why don't electrons from higher energy orbitals cascade into
unpaired states of lower energy?
Jimcsc@watmath.UUCP (Computer Sci Club) (02/12/84)
The Zeeman effect does not create new states, it changes the energy
levels of existing states in such a way that states that before had
the same energy level now have different energy levels.
One of the quantum numbers that determines the state of an electron
is the spin. It can have one of two values +1/2 or -1/2. Now for
every combination of quantum numbers other than spin, there exists
two STATES, one corresponding to each value of the spin quantum number.
In the absence of an external field an electron in either of the states
would have the same energy, reffered to as (twofold) degeneracy. This
leads to the erroneous impression that two fermions can occupy any
energy level. In fact only one electron can occupy each state. The
number of electrons that can occupy a single energy level depends
on the energy level of the states, which depend on many things, including
external fields.
In the presence of an external magnetic field two states which
differ only in the spin quantum number no longer have the same energy
level associated with them. (One gets slightly higher, the other
slightly lower) However as no new states are created, if the lower
energy states were full before the field was applied they will be
full after the field is applied and electrons will not cascade down.
William Hughespalmer@uw-june (David Palmer) (02/13/84)
bitals cascade into
unpaired states of lower energy?
Jim <Stekas>
The Pauli principle states that no two Fermions can be in the same
state at the same time (same state == same wave function, same type of
particle, and same spin direction.) However, the quantum mechanics of
the system says that a particle may only be in certain discrete states
at any one time, and those states depend on the direction of the
particle's spin. In a magnetic field, a particle with spin up cannot
have the same wave function as a particle with spin down, because the
magnetic field acts on the particles differently.
David Palmerbill@utastro.UUCP (William H. Jefferys) (02/13/84)
>> Everyone knows that Fermions obey Pauli statistics - i.e. no two >> Fermions can be in the same state at the same time. That is why >> atomic orbitals become filled when 2 electrons (of opposite spin) >> occupy them. >> >> Now, when an atom is in a magnetic field the spectral lines get split >> due to the Zeeman effect. So what used to be identical electron states >> (except for spin) are now correspond to entirely different energy levels. >> Question - since the electrons in these new states now have no Pauli >> partners, why don't electrons from higher energy orbitals cascade into >> unpaired states of lower energy? There is a confusion here between "energy levels" and "states". The correct rule is that no two fermions can be in the same state, as Jim says in the first line. In an unperturbed atom there are two distinct states of lowest energy which are distinguished only by the spin of the electron. The energies of these two states just happen to be the same. When a magnetic field is introduced, the energies of these two states are different because the magnetic moment of the electron in the two spin states interacts with the external magnetic field differently. There are still only two states, except now their energies are different. -- Bill Jefferys 8-% Astronomy Dept, University of Texas, Austin TX 78712 (USnail) {ihnp4,kpno,ctvax}!ut-sally!utastro!bill (uucp) utastro!bill@ut-ngp (ARPANET)