MODERN PHYSICS: IV
6 Quarks
6 leptons (electron, 3 neutrinos, two others)
Hadrons: Baryons (3 quarks) and Mesons (2)
e-
Plus their antiparticles
Four Fundamental forces
Strong Force (gluons)
Weak force (weird particles)
Electromagnetic force (photons)
Gravity (gravitons)
p+
n
p+
e-
n
Wave-Particle Duality of Light
• Einstein’s theory suggests that although a
photon of light has no mass, it does possess
kinetic energy.
• Einstein further predicted that a photon of light
should also have momentum as follows.
p* = hf/c = h/λ
• The fact that a photon can have momentum
again implies that it has particle properties.
*Momentum,
p = mass x velocity
Wave-Particle Duality of Light
The Compton Effect (1922):
E = ½ mve2
p = mve
-
Collision
Incident Photon = X-ray
-
Momentum
p = hf/c
E = hf
Conservation of Energy & Momentum: The energy and
momentum gained by the electron equals the energy and
momentum lost by the photon.
hf/c – hf ‘/c = mve
E = hf ’
p = hf ’/c
Particles vs. Waves (Light)
• Wave Theory:
•
•
•
•
Explained through polarization.
Explained through reflection.
Explained through diffraction & interference.
Explained through refraction.
• Particle Theory:
•
•
•
•
Explained through photoelectric emission.
Explained through the Compton effect.
Explained through reflection.
Explained through refraction.
Wavelike Behavior of Particles
• The photoelectric effect and Compton scattering showed
that electromagnetic radiation has particle properties.
• Could a particle behave like a wave?
– The answer is yes!
p = mv = h/λ
λ = h/mv
Where:
λ = de Broglie wavelength
Wavelike Behavior of Particles
• Proof of the wavelike behavior of particles was made by
diffracting electrons off a thin crystal lattice.
• The particles showed similar interference patterns to light
when passed through a diffraction grating.
Start p. 7 5/19
Particles vs. Waves
Particles
Waves
Mass
Frequency
Size
Wavelength
Kinetic Energy
Amplitude
Momentum
• Physicists have demonstrated that light has both wavelike
and particle characteristics that need to be considered when
explaining its behavior.
• Similarly, particles – such as electrons – exhibit wavelike
behavior.
Earnest Rutherford (1911)
“The Gold Foil Experiment”
• Bombarded gold foil with  particles from the
radioactive decay of uranium238.
• Most of the particles traveled through very thin gold
foil without being deflected.
• Occasionally, particles would deflect, sometimes at
angles > 90o (due to a coulombic repulsive force).
• Results show that the dense positive charge is
centrally located in the nucleus.
• His model is know as the nuclear model and
disproved Thomson’s theory.
The Gold Foil Experiment
• Rutherford's Gold Foil Experiment
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Note: The diameter of the atom was determined to be on the order of
100,000x larger than the nucleus!
Problems with the Nuclear Model
• Electrons are under constant acceleration due to
centripetal force.
• If electrons are accelerating, then they must be
giving off EM radiation that will cover a continuous
band of wavelengths of the EM spectrum.
• If electrons are losing energy, then they would spiral
into the nucleus.
Neils Bohr (1913)
1. Assumed the laws of electromagnetism do not apply inside
an atom. Consequently, an orbiting electron would not lose
energy even though it is accelerating.
2. Only certain orbital radii are possible for an electron,
representing an energy state (mvr = nh/2).
3. Energy is emitted or absorbed when electrons change from
one discrete energy level to another.
–
Energy levels are consistent with Einstein’s theory on the
photoelectric effect where he said that photons have discrete
amount of energy (E = hf).
The Bohr Model of the Atom
• Atoms have discrete energy levels associated with changes in
location of electrons within the atom.
– The lowest energy level is called the “ground state” (All electrons are
in their proper orbitals).
– When an atom is not in the ground state, it is considered to be in an
“excited state”.
– When an electron absorbs energy from a photon of light, it can
transition to another discrete energy level if the energy of the photon
is exactly equal to the difference in energy levels.
– Orbits near the nucleus have less energy than those farther out
because it takes more energy to move an electron further away.
– Note: An atom is in the excited state for a very short period of time
(~10-9 sec.)!
The Bohr Model of the Atom
• The Bohr model of the atom is commonly called the
“planetary model”.
• Electrons travel in well defined orbits around the nucleus of
the atom.
Einstein & Bohr’s Theories Combined
(The Bohr Radius)
• In Bohr model, the centripetal force of the electron is offset
by the electrostatic force.
Fc = mac
mv2
kq2
Fc =
=
(1)
2
r
r
Coulomb’s Law
v
-
Fc
+
Einstein & Bohr’s Theories Combined
(The Bohr Radius)
• The value of r for a given energy level can be shown to be:
rn =
h2
n2
42mkq2
Z
n = 1, 2, 3, …
E = KE + EPE
E = ½mv2 - kq2/r = -½kq2/r (4)
Atomic
Number
• Substituting (3) into (4) yields:
En =
22mkq4
h2
Z2
n2
(3)
Fc
+
(5)
• Substituting for m, k, h and q yields:
En = (-2.18 x 10-18 J)•Z2/n2 or En = (-13.6 eV)•Z2/n2
v
-
The Bohr Model – Energy Level
Diagram for Hydrogen
• To energize an electron
from the ground state to
n = , 13.6 eV of energy
must be supplied.
• Energy required to
remove an electron is
called the ionization
energy.
• Energy levels get closer
together as they
approach the ionization
energy.
Visible
Light
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Increasing 
Bohr Model and Emission Spectra
• Bohr’s theory for the structure of the atom took into consideration
Einstein’s theory of photons and energy as a means to explain why
Hydrogen emits only four different wavelengths of visible light.
• Bohr’s model predicts that photons of energy will be emitted in the form
of light when an electron transitions from a higher energy level to a lower
energy level.
-
• Photon emitted contains a discrete
amount of energy that is specific to the
transition.
-
+
Ei – Ef = hf
Ef
Ei
Ei – Ef = hc/
Bohr Atom and Emission of Light
Visible Spectrum of the Hydrogen
Atom
• The photons of light emitted when going from any energy level to the
ground state emit light in the ultraviolet region.
• The photons of light
emitted when going from
n=5
n=4
other energy levels to the
n=3
2nd energy level will emit
light in the visible light
n=2
region.
+
Red
655nm
blue green
485nm
Dark Blue
433nm
Violet
409nm
n=1
The Energy Levels of the Hydrogen
Per 7
Atom (The Well)
• In order for an electron to change from a
lower energy state to a higher energy
state, the incident photon must have the
exact amount of energy equivalent to the
difference in energy levels of the
hydrogen atom.
Ephoton = Ei – Ef
• For example: an electron transitioning
from the ground state (n=1) to a higher
energy level (n=2) requires a photon of
10.2eV.
– If the photon had only 10eV of energy or
10.5eV of energy, nothing would happen!
Quantization of the Energy Levels of
the Hydrogen Atom
Ephoton = Ei – Ef
• While an electron in a hydrogen atom
transitions from n=1 to n=3 it needs a
photon with exactly 12.09eV (13.60eV –
1.51eV) of energy, how will it return to
the ground state?
• When transitioning back to the ground
state, the electron can take one of 3
possible transitions: 3 – 1, or 3 – 2
followed by 2 – 1.
– Each jump would emit a photon with an
amount of energy equal to the difference
between the two energy levels.
Problems with the Bohr Planetary
Model
1. The Bohr model of the atom works for Hydrogen,
but not for other elements.
2. Bohr could not explain the conflict between
acceleration of a charged particle (e-) and the
production of EM radiation that would lead to the
collapse of the atom.
Quantum Model (Heisenberg Uncertainty
Principle) - 1926
• Erwin Schroedinger and Werner Heisenberg developed a theoretical
framework that established a new branch of physics called quantum
mechanics.
• Their theories explain the probability of determining a particle’s
position and momentum at the same time.
h
(p y )(y ) 
4
– y=uncertainty of a particle’s position in the y-direction
– py=uncertainty of the y-component of linear momentum
Note: it is not possible to determine the position
and momentum of an electron at the same time!
Quantum Model (Heisenberg Uncertainty
Principle) - 1926
• The quantum model predicts the “probability” of finding the
electron around the nucleus of a atom.
• The probability of finding an electron is its highest in a region
called the electron cloud.
Electron Cloud
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We like to think of electrons as being in pretty “orbits”. We like to think
of electrons as particles, but they also act like waves and spend part of
the time inside the nucleus!
Electrons act like waves that move in specific resonant frequencies.
There is a “fundamental state” (ground state) that is close to the atom.
As energy is added to the electron, it is added in discrete “chunks” – too
little energy cannot be absorbed, too much energy and some of it goes
into increasing the “harmonic” of the electron and some isethrown away.
-
Energy is quantized at the atomic level.
p+
n
p+
e
n
All of the known energy in the universe comes from the conversion of mass into
energy
In stars,
Fusion turns hydrogen into Helium (with several stops along the way)
Fusion turns Helium into Carbon and Nitrogen and Oxygen and … Iron
- When stars run out of Helium they blow up
- Spewing all the bits into space!
e-
p+
n
p+
e-
n
Key Ideas
• The Bohr model of the hydrogen atom contains electrons
which orbit the nucleus in orbits that are associated with
discrete energy levels.
• Erwin Schroedinger and Werner Heisenberg developed the
quantum model of the atom with the wave-particle theory.
• An electron in any state other than the ground state is said to
be excited.
• When an electron transitions from an excited state to the
ground state, it will emit a photon of light and vice-versa
when going from the ground state to an excited state.
Key Ideas
• The atom is defined as a probability cloud of electrons with a
centrally located nucleus.
• The nucleus is fractionally smaller compared to the entire
atom (1/100,000th).
• J.J. Thompson developed the first working model of the atom
– the plum-pudding model.
• Earnest Rutherford developed the nuclear/planetary model of
the atom as a result of the gold foil experiment.
• Neils Bohr further developed the planetary model of the atom
and solved many questions about the hydrogen atom.
Covered Standards:
Mon 5/7
5.3f Among other things, mass-energy and charge are conserved at all levels (from
subnuclear to cosmic).
5.3g The Standard Model of Particle Physics has evolved from previous attempts to
explain the nature of the atom and states that: • atomic particles are composed of
subnuclear particles • the nucleus is a comglomeration of quarks which manifest
themselves as protons and neutrons • each elementary particle has a corresponding
antiparticle
Stress Tues 5/8:
5.3b Charge is quantized on two levels. On the atomic level, charge is restricted to
multiples of the elementary charge (charge on the electron or proton). On the
subnuclear level, charge appears as fractional values of the elementary charge
(quarks).
5.3j The fundamental source of all energy in the universe is the conversion of mass
into energy.*
Covered Standards:
Wed 5/9
5.3j The fundamental source of all energy in the universe is the conversion of mass
into energy.*
5.3a States of matter and energy are restricted to discrete values (quantized).
5.3c On the atomic level, energy is emitted or absorbed in discrete packets called
photons.*
5.3 Compare energy relationships within an atom’s nucleus to those outside the
nucleus. i. interpret energy-level diagrams ii. correlate spectral lines with an energylevel diagram
observe and explain energy conversions in real-world situations recognize and
describe conversions among different forms of energy in real or hypothetical devices
such as a motor, a generator, a photocell, a battery
4.1b Energy may be converted among mechanical, electromagnetic, nuclear, and
thermal forms.
4.3a An oscillating system produces waves. The nature of the system determines the
type of wave produced.
4.3d Mechanical waves require a material medium through which to travel.
4.3g Electromagnetic radiation exhibits wave characteristics. Electromagnetic waves
can propagate through a vacuum.
4.3l Diffraction occurs when waves pass by obstacles or through openings. The
wavelength of the incident wave and the size of the obstacle or opening affect how
the wave spreads out.
4.3 Explain variations in wavelength and frequency in terms of the source of the
vibrations that produce them, e.g., molecules, electrons, and nuclear particles. iv.
differentiate between transverse and longitudinal waves
5.3h Behaviors and characteristics of matter, from the microscopic to the cosmic
levels, are manifestations of its atomic structure. The macroscopic characteristics of
matter, such as electrical and optical properties, are the result of microscopic
interactions.
5.3i The total of the fundamental interactions is responsible for the appearance and
behavior of the objects in the universe.
5.3d The energy of a photon is proportional to its frequency.* 5.3e On the atomic
level, energy and matter exhibit the characteristics of both waves and particles.