Quantum Mechanics Theory that describes the physical properties
of smallest particles (atoms, protons, electrons, photons) "A
scientific truth does not triumph by convincing its opponents and
making them see the light, but rather because its opponents
eventually die and a new generation grows up that is familiar with
it." Max Planck Erwin Schrdinger "I don't like it and I'm sorry I
ever had anything to do with it." "An expert is someone who knows
some of the worst mistakes that can be made in his subject, and how
to avoid them" Werner Heisenberg "It is true that many scientists
are not philosophically minded and have hitherto shown much skill
and ingenuity but little wisdom." Max Born
Slide 3
The hydrogen atom Niels Bohr (1885-1962) - electron orbits
around the nucleus like a wave - orbit is described by wavefunction
- wavefunction is discrete solution of wave equation - only certain
orbits are allowed - orbits correspond to energy levels of
atom
Slide 4
The hydrogen atom In the Bohr model of the atom, the hydrogen
atom is like a planetary system with the electron in certain
allowed circular orbits. The Bohr model does not work for more
complicated systems!
Slide 5
Quantum numbers Each orbital is characterized by a set of
quantum numbers. Principal quantum number (n): integral values
(1,2,3). Related to the size and energy of the orbital. Angular
momentum quantum number ( l ): integral values from 0 to (n-1) for
each value of n. Magnetic quantum number (m l ): integral values
from - l to l for each value of n.
Slide 6
Quantum numbers How many orbitals are there for each principle
quantum number n = 2 and n = 3? For each n, there are n different
l-levels and (2l+1) different m l levels for each l. n=2:n =
2different l-levels (2l+1) = 2 x 0 + 1= 1 m l -levels for l = 0 l =
0, 1 (2l+1) = 2 x 1 + 1= 3 m l -levels for l = 1 Total: 1 + 3 = 4
levels for n = 2
Slide 7
Quantum numbers How many orbitals are there for each principle
quantum number n = 2 and n = 3? For each n, there are n different
l-levels and (2l+1) different m l levels for each l. n=3:n =
3different l-levels (2l+1) = 2 x 0 + 1= 1 m l -levels for l = 0 l =
0, 1,2 (2l+1) = 2 x 1 + 1= 3 m l -levels for l = 1 Total: 1 + 3 + 5
= 9 levels for n = 3 (2l+1) = 2 x 2 + 1= 5 m l -levels for l = 2
The total number of levels for each n is n 2
Slide 8
Quantum numbers Names of atomic orbitals are derived from value
of l :
Slide 9
Quantum numbers Quantum numbers for the first four levels in
the hydrogen atom.
Slide 10
What is the meaning of ? Wavefunction itself is not an
observable! Square of wavefunction is proportional to probability
density I cannot but confess that I attach only a transitory
importance to this interpretation. I still believe in the
possibility of a model of reality - that is to say, of a theory
which represents things themselves and not merely the probability
of their occurrence. On the other hand, it seems to me certain that
we must give up the idea of complete localization of the particle
in a theoretical model. This seems to me the permanent upshot of
Heisenberg's principle of uncertainty. (Albert Einstein, on Quantum
Theory, 1934
Slide 11
Wavefunction and probability function r probability
Slide 12
Quantum numbers A subshell is a set of orbitals with the same
value of l. They have a number for n and a letter indicating the
value of l. l = 0 (s) l = 1 (p) l = 2 (d) l = 3 (f) l = 4 (g)
Slide 13
Orbital Shapes
Slide 14
Heisenberg uncertainty principle Life is uncertain! Wheres the
electron? Werner Heisenberg Thats quite uncertain!
Slide 15
Heisenberg uncertainty principle It is not possible to know
both the position and momentum of an electron at the same time with
infinite precision. x is the uncertainty in position. (mv) is the
uncertainty in momentum. h is Plancks constant.
Slide 16
Heisenberg
Slide 17
The s orbitals in hydrogen The higher energy orbitals have
nodes, or regions of zero electron density. orbital surfaces
probability distributions s-orbitals have n-1 nodes. The 1s orbital
is the ground state for hydrogen. The orbital is defined as the
surface that contains 90% or the total electron probability (
).
Slide 18
Pauli exclusion principle How many electrons fit into 1
orbital? m s = +1/2m s = -1/2 Only 2 electrons fit into 1 orbital:1
spin up 1 spin down
Slide 19
Pauli exclusion principle As the temperature is lowered, bosons
pack much closer together, while fermions remain spread out.
Electrons are fermions. There are also bosons
Slide 20
Energy Levels n =1 n =2 n =3 n =4 n =5 n = E R H = 2.178 x 10
-18 J Z = atomic number n = energy level
Slide 21
Energy Transitions For the energy change when moving from one
level to another: n =1 n =2 n =3 n =4 n =5 n = E transition
Slide 22
Lines and Colors Change in energy corresponds to a photon of a
certain wavelength: Change in energy Frequency of emitted light
Wavelength of light emitted
Slide 23
Lines and Colors What is the wavelength of the photon that is
emitted when the hydrogen atom falls from n=3 into n=2? nm
Slide 24
Light out of Molecules n =1 n =2 n =3 n =4 n =5 n = E
transition hydrogen Rhodamine 532 nm 570 nm Fluorescence
Slide 25
Degeneracy Orbital energy levels for the hydrogen atom.
Slide 26
Beyond hydrogen Hydrogen is the simplest element of the
periodic table. Exact solutions to the wave equations for other
elements do not exist!
Slide 27
Polyelectric Atoms What do the orbitals of non-hydrogen atoms
look like? Multiple electrons: electron correlation Due to electron
correlation, the orbitals in non-hydrogen atoms have slightly
different energies
Slide 28
Polyelectric Atoms Screening: due to electron repulsion,
electrons in different orbits feel a different attractive force
from the nucleus 11 + e-e- e-e- e-e- e-e- e-e- e-e- e-e- e-e- Sees
a different effective charge! Screening changes the energy of the
electron orbital; the electron is less tightly bound.
Slide 29
Polyelectric Atoms Penetration: within a subshell (n), the
orbital with the lower quantum number l will have higher
probability closer to the nucleus n =2 orbital n=3 orbital
Slide 30
Polyelectric Atoms Hydrogen Polyelectric atom Orbitals with the
same quantum number n are degenerate Degeneracy is gone: E ns <
E np < E nd < E nf
Slide 31
Spectra of Polyelectric Atoms Due to lifting of degeneracy,
many more lines are possible in the spectra of polyelectric
atoms