Download Complete nomenclature for electron orbitals

Complete nomenclature for electron orbitals
Enter de Broglie again
l Bohr’s model worked
but it lacked a
satisfactory reason
why.
l De Broglie suggested
that all particles have
a wave nature.
u
l=h/p
It was the Wave Nature of the
electron that determined the
nature of the orbits.
de Broglie waves
• One of postulates of
Bohr’s ‘ugly theory’ was
that angular momentum
of the hydrogen atom is
quantized: mevr = nh
• Why? Not known for 10
years until de Broglie
gave a physical
interpretation.
• Electron orbit could be
stable only if an integral
number of electron
wavelengths could be fit
inside orbit.
• 2pr = nl n=1,2,3,…
de Broglie waves
l 2pr = nl
l l=h/mev (de Broglie
wavelength)
l Plug into top equation
u
u
2pr=nh/mev…or
mevr=nh/(2p)
l De Broglie was able to
explain the appearance
of integers in the Bohr
theory as a natural
consequence of standing
wave patterns
3 wavelengths
so n=3
Spin magnetic quantum number
l Another puzzle: close
examination of one of the
prominent lines in the sodium
spectrum shows that it is
actually 2 very closely spaced
lines
l No way of understanding this
split
l Uhlenbeck and Goudsmit
suggested that there was a
4th quantum number, the spin
quantum number, that needed
to be introduced
l Can think of the electron as
spinning on its axis
u
u
u
it can either spin up or spin
down
no other possibilities
ms=+1/2 (spin up); ms=-1/2
(spin down)
Quantum model of atom
l The previous picture is still a
little too classical, though
l It pictures the electrons as
orbiting the nucleus in circular
(or elliptical orbitals)
l But in fact the only reality is
|y|2, the square of the
wavefunction, which gives the
probability of the electron to
be in a given place at a given
time
l Electron is not confined to any
particular orbital distance from
the nucleus but has a
probability of being at various
distances (with a maximum
probability at the Bohr radius
ao)
l Think of the electron as being
in an electron cloud
|y|2 for ground state
of hydrogen
Electron clouds
l For hydrogen, the
electron cloud looks
simple (spherically
symmetric)
l Not so simple for
other atoms like
carbon
u
lot of interesting
chemistry
Picture of atom-1920’s
Pauli exclusion principle
l Each electron in a
hydrogen (or any other
type of atom) can be
specified by the quantum
numbers: n,l,ml and ms
l Wolfgang Pauli (one of
founders of quantum
mechanics) discovered
that no two electrons in
the same atom can ever
have exactly the same
values for the set of
quantum numbers
u
u
Pauli exclusion principle
helps to explain the
electronic structure of
complex atoms
Filling electron shells
l As one goes through the
periodic table towards higher
Z, electrons fill in each subshell starting from the lowest
energy level
l Each subshell has 2(2l+1)
electrons in it
l H (1 electron) is described by
either of quantum numbers
(1,0,0,1/2) or (1,0,0,-1/2)
u 1s1
l He (2 electrons) is described
by quantum numbers
(1,0,0,1/2) and (1,0,0,-1/2)
u 1s2
l Li (3 electrons) has 2
electrons in the 1s subshell
and 1 electron in 2s subshell
u 1s22s1
Electronic configurations
Atomic transitions
Consider the possible energy levels of the
electrons in an atom. If light is incident on
this atom, only photons with an energy equal
to the difference DE between two of the
energy levels can be absorbed
At room temperature, most of the time the
atom is in its ground state, so incident photon
energies have to correspond to E2-E1,
E3-E1, etc
Known as stimulated absorption.
Spontaneous emission
Once an electron is in an excited state, it can fall back to the ground state, emitting a photon.
Stimulated emission
l Suppose an atom is in an
excited state E2 and a photon
with energy hf=E2-E1 is
incident on the atom
l Incoming photon of this
energy increases the
probability of the atom
returning to the ground state
emitting a photon of the same
energy hf as the incident
photon and in phase with the
incident photon
l These photons can then
stimulate other atoms to emit
photons
l The end result can be an
intense (many photons),
coherent (all photons in phase
and of same wavelength)
burst of light
Laser (light amplification by stimulated emission of radiation)
Bands and band gaps
l If we have a single atom, then
we’ve learned about the
energy levels possible for
electrons in the atom
l If we have many atoms close
together (like in a solid), the
energy levels smush out into
bands
u electrons in the solid can
have energies within the
bands
u …and the energies
between the bands are
forbidden (band gaps)
u highest filled band (in
ground state) is called
valence band
u next higher empty band is
called conduction band
Conductors and insulators
Suppose I apply a voltage across a conductor.
What happens? Some of the electrons can
accelerate and gain energy. This is possible
because the conduction band is close in energy
to the valence band and there are empty
energy states to jump into. This can’t happen
with insulators where there is too large of an
energy gap between.
Semi-conductors
l In between a conductor
and an insulator is a
semi-conductor where
there is a small band gap
of about 1 eV
u
u
silicon
gallium arsenide
l The size of the band gap
energy Eg depends on
the temperature of the
semiconductor