*
* Max Planck proposed that an atom can absorb or emit
energy only in chunks known as quanta.
* The energy, E ,of each quantum depends on the frequency of
the radiation
E= hf
h= 6.626 x 10-34 J·s (Planck’s constant)
* Einstein suggested that a fundamental property of
electromagnetic radiation consists of quanta of energy
known as photons.
E = hf = hc/λ
PHOTO-ELECTRIC EFFECT
Einstein used the photon hypothesis to explain the Photoelectric effect (
emission of electrons from a metal surface when a light is incident on it)
* In this “quantum-mechanical” picture, the energy of the
light particle (photon) must overcome the binding energy of the
electron to the nucleus.
*
If the energy of the photon exceeds the binding energy, the
electron is emitted with a KE = Ephoton – Ebinding.
“Light particle”
Before Collision
After Collision
THE ELECTROMAGNETIC SPECTRUM
Shortest wavelengths
(Most energetic photons)
E = hn = hc/l
h = 6.6x10-34 [J*sec]
(Planck’s constant)
Longest wavelengths
(Least energetic photons)
There is a threshhold negative potential, the stopping
potential, V0 , below which no current will flow into the circuit
Each light intensity has a maximum current flow, but the
stopping potential remains the same
* When V is negative, only electrons with a kinetic energy greater
than |eV0| can reach the anode, the maximum kinetic energy is
given by eV0 .
* ( ½ mv2 )max = eV0 = hf –φ
* φ = work function ( energy needed to release an electron from
the metal)
* Special relativity -
the laws of physics are
same in all inertial frames of reference
* Invariance of c -
the speed of light in a
vacuum is a universal constant ( c ) which is
independent of the motion of the light source
*
* Lorentz contraction
* An observer moving with respect to an object will observe it
to be contracted along the direction of motion by the factor
* A perceived reduction in the length of an object
* Negligible at the speeds we experience everyday but would
be noticeable at velocities comparable to that of light
For more information see http://www.fourmilab.ch/cship/lorentz.html
Time dilation
The time lapse between two events is dependent on the relative
speeds of the observer’s reference frames
*
* The total energy of a mass m moving at a velocity v is given
by
𝐸=
𝑚𝑐 2
𝑣2
1− 2
𝑐
* So when v = 0 , E= mc2
*
α Alpha particles are produced from the
radioactive decay of heavy elements such as
uranium. They are composed of two neutrons
and two protons identical to the nucleus of a
helium atom. Because of their relative size and
electrical charge from the two protons, alpha
particles can travel only a very short distance in
any material. For example a normal sheet of
paper can stop alpha particles.
β Beta particles are electrons that come from transformation of a neutron in
the nucleus of an atom to a proton. They can travel up to about five meters in
air and one centimeter in tissue.
g Gamma rays are electromagnetic radiation similar to X-rays. Unlike the latter,
which are produced by machines, gamma rays are emitted from the nucleus of a
radioactive atom that is in an excited state. Gamma rays travel at the speed of
light and can penetrate long distances in air and tissue. Several centimeters of
lead or meters of water are needed to stop typical gamma rays
a decay
241
95
a
4
Am 
 237
Np

93
2 He
- involves strong and coloumbic forces
- alpha particle and daughter nucleus have equal and opposite momentums
(i.e. daughter experiences “recoil”)
 decay - three types
1) - decay
3
1

H 
 23 He  e   e
- converts one neutron into a proton and electr
- no change of A, but different element
- release of anti-neutrino (no charge, no mass)
2) + decay

C  115 B  e  e
11
6
- converts one proton into a neutron and electr
- no change of A, but different element
- release of neutrino
3) Electron capture
7
4
EC
Be  e  
 37 B  e
g decay
3
2
g
He* 
 23 He  g
- conversion of strong to coulombic E
- no change of A or Z (element)
- release of photon
- usually occurs in conjunction with other deca
Spontaneous fission
256
100
sf
112
Fm 
 140
Xe

54
46 Pd  4n
- heavy nuclides split into two daughters
and neutrons
- U most common (fission-track dating)
Fission tracks from 238U fission in old zircon
*
* The time it takes for one half of the sample to
decay
*
Activity calculations
Activity  l N
- usually reported in dpm (disintegrations per minute),
example: 14C activity = 13.56 dpm / gram C
A  A0e  lt
- because activity is linerarly proportional to number lN,
t
N

N
e
0
then A can be substituted for N in the equation
Example calculation:
How many 14C disintegrations have occurred in a 1g wood sample formed in 1804AD?
T=200y
t1/2 = 5730y so l = 0.693/5730y = 1.209e-4 y-1
N0=A0/l
so N0=(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e-4= 5.90e10 atoms
N(14C)=N(14C)0*e-(1.209e-4/y)*200y = 5.76e10 atoms
# decays = N0-N = 2.4e9 decays
*
*Models of the Atom
a Historical
Perspective
*Early Greek Theories
* 400 B.C. - Democritus thought matter could not be
divided indefinitely.
• This led to the idea of atoms in a void.
fire
Democritus
earth
Aristotle
air
water
• 350 B.C - Aristotle modified an earlier
theory that matter was made of four
“elements”: earth, fire, water, air.
• Aristotle was wrong. However, his
theory persisted for 2000 years.
*John Dalton
* 1800 -Dalton proposed a modern atomic model
based on experimentation not on pure reason.
•
•
•
•
All matter is made of atoms.
Atoms of an element are identical.
Each element has different atoms.
Atoms of different elements combine
in constant ratios to form compounds.
• Atoms are rearranged in reactions.
• His ideas account for the law of conservation of
mass (atoms are neither created nor destroyed)
and the law of constant composition (elements
combine in fixed ratios).
*Adding Electrons to the Model
Materials, when rubbed, can develop a charge
difference. This electricity is called “cathode rays” when
passed through an evacuated tube (demos).
These rays have a small mass and are negative.
Thompson noted that these negative subatomic particles
were a fundamental part of all atoms.
1) Dalton’s “Billiard ball” model (1800-1900)
Atoms are solid and indivisible.
2) Thompson “Plum pudding” model (1900)
Negative electrons in a positive framework.
3) The Rutherford model (around 1910)
Atoms are mostly empty space.
Negative electrons orbit a positive nucleus.
Ernest Rutherford
Rutherford shot alpha (a) particles at gold foil.
Zinc sulfide screen
Thin gold foil
Lead block
Radioactive
substance
path of invisible aparticles
Most particles passed through. So, atoms
are mostly empty.
Some positive a-particles deflected or
bounced back!
Thus, a “nucleus” is positive & holds most
of an atom’s mass.
Bohr’s model
• Electrons orbit the nucleus in “shells”
• Electrons can be bumped up to a higher shell if hit
by an electron or a photon of light.
There are 2 types of spectra: continuous spectra & line spectra.
It’s when electrons fall back down that they release a photon.
These jumps down from “shell” to “shell” account for the line
spectra seen in gas discharge tubes (through spectroscopes).
*Quantum Numbers:
* n = principal quantum number
*
* l = azimuthal quantum number
* (orbital angular momentum)
* ml = magnetic quantum number
* ms = spin magnetic quantum number
*
Quantum Mechanics and Atomic Orbitals
Orbitals and Quantum Numbers
Representations of Orbitals
The s-Orbitals
Representations of Orbitals
The p-Orbitals
d-orbitals
Many-Electron Atoms
Electron Spin and the Pauli Exclusion
Principle
The smallest pieces of
matter…
• Nuclear physics and
particle physics
study the smallest
known building
blocks of the
physical universe -and the interactions
between them.
• The focus is on
single particles or
small groups of
particles, not the
billions of atoms or
molecules making up
Further layers of substructure:
u quark:
electric
charge = 2/3
d quark:
electric
charge = -1/3
Proton = uud
electric charge = 1
Neutron = udd electric
charge = 0
www.cpepweb.org
If each proton were 10 cm across, each quark would be .1 mm in
size and the whole atom would be 10 km wide.
Introducing the neutrino
Another subatomic
particle, the
neutrino, plays a
crucial role in
radioactive decays
like n -> p+ + e- +
The ve (electron-neutrino) is closely related v
toethe electron but has
strikingly different properties.
Name
Mass
electron
0.0005 GeV
electron-neutrino < 0.00000001 GeV
Electric Charge
-1
0