Transcript File

Atomic Physics
Quantization of Energy
Atomic Models
Quantum Mechanics
Electric and Magnetic Fields
Summary
• A changing magnetic field can induce a current in a
circuit (Faraday’s Law of Induction)
• A magnetic field is created around a current-carrying
wire (Ampere’s Law)
• Electric field lines start on positive charges and end at
negative charges (Coulomb’s Law / Gauss’s Law)
• Magnetic field lines always form closed loops with no
beginning and no end (Gauss’s Law for magnetism)
• These unrelated observations, experiments and
equations were all known by the mid-1800s, but nothing
linked them together.
Maxwell’s Equations
• James Clerk Maxwell (1831-1879)
– Scottish theoretical physicist & mathematician
• Maxwell’s Equations
– Set of differential equations that describe the
relationship between electric and magnetic
field
– Summarized all previous work of Coulomb,
Ampere, Gauss, Faraday & others
Maxwell’s Equations
Name
Differential form
Integral form
Gauss's law:
Gauss's law for
magnetism:
Maxwell-Faraday
equation
(Faraday's law
of induction):
Ampère's circuital
law
(with Maxwell's
correction):
Relax!!! You don’t need to use these.
Maxwell’s Equations
• Predicted:
– a changing magnetic field would create a changing
electric field, which would, in turn, create a changing
magnetic field, and so on
– existence of electromagnetic waves that move
through space at the speed of light
– light is an electromagnetic wave
• Confirmed:
– Heinrich Hertz in 1887
– generated and detected the first E/M waves
Electromagnetic Waves
• Oscillating electric
and magnetic fields
• E-field and B-field are
at right angles to each
other
• Propagates at a right
angle to both fields
(transverse wave)
Electromagnetic Waves
• EM waves can be produced most easily by
an oscillating charged particle
• Frequency of oscillation determines
frequency of the EM wave
• Wavelength related to frequency by:
  c/ f
c  3.0 x 10 m/s
8
Electromagnetic Radiation
• Energy is the ability to do work
• E-fields & B-fields store energy because they
exert a force (do work) on charged particles
• Electromagnetic Radiation:
– transfer of energy associated with electric and
magnetic fields
– can be transferred to objects in the EM wave’s path
– can be converted to other forms, such as heat
– Continuous distribution of wavelengths on the
electromagnetic spectrum.
Electromagnetic Spectrum
Blackbody Radiation
• All objects emit electromagnetic radiation
– Continuous distribution of wavelengths from
the infrared, visible, and UV portions of the
EM spectrum
– Intensity distribution of different wavelengths
varies with temperature
– At low temps: mostly infrared (invisible)
– Temp increases: distribution shifts to visible &
UV
– Metals glow: red > yellow > white > blue
Blackbody Radiation
• Most objects absorb some incoming radiation
and reflect the rest
• Blackbody:
–
–
–
–
Ideal system that absorbs all incoming radiation
Hollow object with a small opening
Perfect absorber and perfect radiator
Emits radiation based only on its temperature
• In 1900, Max Planck (1858-1947), proposed that
the walls of a blackbody contained billions of
submicroscopic electric oscillators, which he
called resonators. These resonators, produced
the blackbody radiation.
Blackbody Radiation
Classical Theory
Exper. Data / Planck’s Theory
as wavelength approaches zero,
the amount of energy should
become infinite
as wavelength approaches zero,
the amount of energy radiated also
approaches zero
energy absorbed and emitted by a
single resonator is continuous
energy absorbed and emitted by a
single resonator occurs in certain
discrete amounts
Quantization of Energy
• Planck found that the total energy of a resonator
is an integer multiple of the frequency
• Because the energy of each resonator comes in
discrete units, it is said to be quantized.
• Allowed energy states are called quantum states
or energy levels.
• Einstein applied the concept of quantized energy
to light.
• Photon: quantized unit of light energy
• Photons are absorbed or given off by electrons
“jumping” from one quantum state to another.
Quantization of Energy
Total Energy of a Resonator :
En  nhf
n : quantum number; positive integer
h : Planck' s constant; 6.63 x 10-34 J  s
Energy of a Light Quantum :
(energy difference between tw o adjacent levels)
E  hf
Measure atomic energy in electron v olts :
1 eV  1.60 x 10-19 J
The Photoelectric Effect
When light strikes a metal surface, the surface may
emit electrons, called photoelectrons.
• Classical physics predicts:
– Light waves of any frequency
should have enough energy to
eject electrons if the intensity is
high enough
– At low intensities, electrons should
be ejected if light shines on the
metal for a long enough period of
time
– Increasing the intensity of the light
waves should increase the kinetic
energy of the photoelectrons.
– Maximum kinetic energy of a
photoelectron should be
determined by the light’s intensity
The Photoelectric Effect
• Experimental evidence shows that:
– No photoelectrons emitted if the light frequency falls
below a certain threshold frequency, even if the intensity
is very high
– Threshold frequency, ft, depends on material
– If light frequency exceeds ft
• # of photoelectrons emitted is proportional to light intensity
• Maximum kinetic energy of photoelectrons is proportional to the
frequency and is independent of the intensity
• Electrons are emitted instantaneously, even at low intensities
• Classical physics could not explain the photoelectric
effect … but Einstein could!
Einstein’s Explanation
• EM waves are quantized
• Think of light as a stream of particles,
called photons
• Photon energy given by Planck’s equation
• When photons collide with electrons in
metal, they transfer energy to electrons
E photon  hf
Einstein’s Explanation
• If photon energy is
greater than work
function of the metal,
photoelectrons are
ejected
• If photon has more
energy than the work
function, the difference
is the kinetic energy of
the photoelectrons
ejected from the
surface
Maximum KE of Photoelectrons
KEmax  hf  hf t
KEmax : maximum KE of photoelect rons
hf : energy of incoming photon
hf t : work function of metal
f t : threshold frequency
Compton Shift
• American physicist Arthur
Compton (1892-1962)
proposed that momentum &
energy should be conserved
in a collision between photons
& electrons
• After a collision, scattered
photon should have a lower
energy, therefore a lower
frequency (longer wavelength)
• In 1923, conducted
experiments with X rays to
demonstrate this change in
wavelength, known as
Compton shift.
Models of the Atom
• Thomson Model /
“Plum Pudding”
Model
– Discovery of electron
in 1897
– Negative electrons in
sphere of positive
charge
Models of the Atom
• Rutherford Model /
Planetary Model
– 1911 experiment by
Geiger & Marsden
demonstrated that
practically all of atom’s
mass and all positive
charge must be centrally
located in atom
(nucleus)
– Electrons orbit nucleus
like planets around Sun
Problems with the
Rutherford Model
• Electrons orbiting the nucleus would undergo
centripetal acceleration
• Accelerating electrons would radiate EM waves
• Electrons radiating EM waves would lose energy
• Loss of energy would cause electron’s orbital
radius to drop
• Frequency of emitted radiation would increase
• Electrons would rapidly collapse into nucleus
Need a better model!
Atomic Spectra
•
•
•
•
•
Fill a glass tube with pure atomic gas
Apply a high voltage between electrodes
Current flows through gas & tube glows
Color depends on type of gas
Light emitted is composed of only certain wavelengths
Atomic Spectra
• Emission Spectrum: diagram or graph that
indicates the wavelengths of radiant energy that a
substance emits (bright lines)
• Absorption Spectrum: same thing, just for light
absorbed by a substance (dark lines)
What does this have to do with atomic models?
The Bohr Model
• Similar to Rutherford’s model, but only allows certain,
discrete orbits
• Electrons are never found between orbits, but can
“jump” from one orbit to another
• Electrons only emit radiation when they jump from an
outer orbit to an inner one
• Energy of emitted photon is equal to energy decrease
of electron. This determines frequency of emitted
radiation.
• Energy of emitted photon is quantized – only certain
quantities are allowed. Hence, electrons undergo
“quantum leaps”. (Obligatory pop culture reference)
E photon  Einitial  E final  hf
Energy Levels & Emission Spectra
• Lowest energy state: ground state
– Radius of this state: Bohr radius
– Electrons usually here at ordinary temps
• How do electrons “jump” between states?
– Absorb photon with energy (hf) exactly equal to
energy difference between ground state & excited
state
– Absorbed photons account for dark lines in absorption
spectrum
Energy Levels & Emission Spectra
• Spontaneous emission:
– Electron in excited state
jumps back to a lower
energy level by emitting a
photon
– Does NOT need to jump
all the way back to the
ground state
– Emitted photon has
energy equal to energy
difference between levels
– Accounts for bright lines
on emission spectrum
– Jumps between different
energy levels correspond
to various spectral lines
The Bohr Model
Successes
• Account for wavelengths
of all spectral lines of
hydrogen
• Provides explanation for
auroras
• Gave expression for
radius of hydrogen atom
• Predicted energy levels of
hydrogen
• Also successful when
applied to hydrogen-like
atoms (only one electron)
Failures
• Unsuccessful when
applied to multi-electron
atoms
• Did not explain why
electrons do not radiate
energy when in a stable
orbit
• Did not explain why other
orbits do not occur
• Combined classical and
non-classical physics
The Dual Nature of Light
• Is light a particle or a wave?
– Particle: blackbody radiation, photoelectric effect
– Wave: interference, diffraction
• Which model is correct?
– Both are correct, but depends on the situation
– Each phenomenon exhibits only one or the other
natures of light
– True nature of light is not describable in terms of
a single classical idea
The Dual Nature of Light
Low Frequency Light
(Wave Nature)
• Very low energy
– Difficult to detect a single
photon
– Photon nature of light not
evident
• Long wavelength
– Wave effects, like
diffraction and interference
are easy to observe
High Frequency Light
(Photon Nature)
• Very high energy
– Easy to detect single
photons
– Photon nature of light is
evident
• Short wavelength
– Wave effects, like
diffraction and interference
are more difficult to
observe
Matter Waves
• Since light can be described as either a
particle or a wave, can we do the same for all
objects, like atoms and people and cars?
• Louis de Broglie thought so!
• In 1924, proposed that all matter may have
wave properties and particle properties
• Matter has a dual nature, just like light!
• Proposed idea of matter waves
Matter Waves
• The larger the momentum of an object, the
smaller its wavelength
Matter Waves
• Frequency of matter waves can be found
with Planck’s equation
Evidence for Matter Waves
• 1927: Davisson & Germer, showed that electrons can
be diffracted by a single crystal of nickel
• Electron diffraction is possible because the de Broglie
wavelength of an electron is approx. equal to distance
between atoms (the size of the diffraction grating)
• Large-scale objects don’t demonstrate this well
because large momentum generates wavelengths
much smaller than any possible aperture through
which the object could pass (won’t be diffracted)
Bohr Model Explained
• De Broglie hypothesized that only certain
electron orbits are stable
• Circumference of orbit must contain an
integral multiple of electron wavelengths
• Similar to standing waves on a string
The Uncertainty Principle
• Wave nature of particles restricts the
precision of our measurements
• Werner Heisenberg (1927):
– It is fundamentally impossible to make
simultaneous measurements of a particle’s
position and momentum with infinite accuracy
– The more we learn about a particle’s
momentum, the less we know of its position,
and vice versa.
The Uncertainty Principle:
A Thought Experiment
• Imagine trying to measure an electron’s
position and momentum with a powerful
microscope
• In order to see the electron, thereby
determining its location, at least one photon
of light must bounce off the electron and pass
through the microscope to your eye
• When the photon strikes the electron, it
transfers some energy & momentum to the
electron. So we are less sure of the
electron’s momentum.
The Uncertainty Principle:
A Thought Experiment
Schrodinger’s Wave Equation
• Erwin Schrodinger (1926) proposed a
wave equation for de Broglie’s matter
waves
• Each particle can be represented by a
wave function , , dependent on the
position of the particle and time
The Electron Cloud
• Max Born (1926) interpreted
Schrodinger’s wave function
to show probability of finding
an electron at certain
locations
• ||2 is proportional to
probability of finding the
electron at a certain position
• Peak probability for an
electron in the ground state
corresponds to Bohr radius
Quantum Mechanical Model
• Electrons are not confined to particular orbital
distances as assumed in Bohr model
• Electron cloud: a probability cloud
– Density at each location related to probability of
finding electron at that location
– Wave function predicts geometry for energy
levels (some spherical, others more complex)
– Most probable location still corresponds to Bohr
radii, but impossible to determine actual location
• Mathematical picture of the atom that
explains certain aspects of atomic structure
that Bohr model cannot explain