Download Quantum Mechanics

Quantum Physics
Quantum Theory
Max Planck, examining heat radiation (ir
light) proposes energy is quantized, or
occurring in discrete small packets with
a definite minimum value. (1901)
All energy amounts were multiple of a
certain constant, called Planck’s
constant h with a value of 6.63 x 10-34
Js
Energy of radiation, E = hf
Max Planck
1858-1947
The Photoelectric Effect
Hertz observed spark discharges
improved with illumination (1898)
Illumination of metal by electromagnetic
radiation causes emission of electrons
Could not be explained by wave theory
Frequency of e-m radiation determines
if emission occurs, not intensity
The Photoelectric Effect
Each metal has minimum energy that must
be supplied by light before emission
occurs: called the work function of the
metal.
Each metal found to have cutoff frequency
of incident light below which no emission
occurs, no matter how intense the light
Only particle theory of light could explain
this
Einstein’s Explanation
Light consists of stream of massless
particles called photons having energy
hf, moving along electromagnetic waves
(1905)
When photon strikes electron, it gives
up all its energy to the electron
If hf > w (work function of metal),
emission occurs
Einstein’s Explanation
Light intensity makes no difference if
frequency is below a threshold
frequency, ft
Work function of metal = h ft
Max. electron kinetic energy = hf - hft
Einstein won Nobel Prize for
explanation
Albert
Einstein
1879-1955
Laws of Photoelectric
Emission
• Rate of emission is directly proportional
to intensity of incident light
• Kinetic energy of photoelectrons is
independent of intensity of incident light.
• Maximum kinetic energy of
photoelectrons varies directly with
difference between frequency of
incident light and cutoff frequency of
metal
Compton Shift
Aurthur Compton sent X-rays into graphite
X-rays scattered by collisions with
electrons showed longer wavelength and
lower energy
Energy and momentum transferred from
photon to electron
Further support for particle nature of light
The Compton Shift
Arthur Compton
1892-1962
The Quantized Atom
Rutherford’s discovery of nucleus (1911)
led to “solar system” model of atom
Orbiting electrons contradicted e-m
theory
Niels Bohr (1913) proposed model of
atom with electron orbits based on
quantized energy states
Difference between energy states always
some multiple of Planck’s constant
Light Emission
Electrons can absorb energy and “jump”
to higher energy level
When electrons fall to lower level,
photon is emitted whose energy equals
difference in the energy of the two
levels
Since frequency depends on energy,
different energy changes cause different
colors (frequencies) of light emitted
Niels Bohr
Ernst Rutherford
1885-1962
1871-1937
Line Spectra
Unique structure of each element
results in unique pattern of emission
lines for each element allowing
identification by spectroscopy
When light passes through the element
(usually as a low pressure gas) same
frequencies are absorbed from the
spectrum
Continuous Spectrum
When atoms are crowded together in a
solid or dense gas, available energy
levels are so numerous, all light
frequencies are emitted
White light is seen and when dispersed
by a prism or diffraction grating, all
colors are seen
The Hydrogen Spectrum
Hydrogen spectrum first to be analyzed
Visible emission lines predicted and
observed by Balmer; called Balmer
series.
6 uv emission lines (Lyman series) and
4 ir lines (Paschen series) discovered
later.
Matter and Waves
de Broglie proposed wave-particle
duality applied to matter particles,
photons must have momentum
E = hf = mc2 ; so mc = h/l , photon
momentum
l = h/mv , wavelength of particle with
mass m and velocity v
Louis de
Broglie
1892-1987
Matter and Waves
All matter has wave properties but for
large objects, wavelength is too small to
be observed
Wave nature of electron explains why
only some orbits are stable: standing
wave must fit in orbit
Whole number of wavelengths must
equal circumference of orbit
Matter Waves
X-Ray Production
Reverse of photoelectric effect
High energy electron beam strike metal
causing emission of photons
EK = hfmax - w
Frequency of photon depends on speed
of electron
Werner
Heisenberg
1901-1976
The Uncertainty
Principle (Heisenberg,
1927)
It is impossible to simultaneously
measure particle’s position and
momentum accurately
Measurement of one quantity changes
the other
Electron’s location can only be
described by probability
Erwin
Schrödinger
1887-1961
The Wave Function
Schrödinger (1926) proposed wave
function (Ψ) that describes subatomic
particles
Probability of electron’s location can be
found using the wave function
Electron orbitals are probability
distributions called electron clouds