Download Figure 30-5 The Photoelectric Effect

Figure 30-1
An Ideal Blackbody
Figure 30-2
Blackbody Radiation
Figure 30-3
The Ultraviolet Catastrophe
Black body radiation
• Black body radiation can be explained by
considering the radiation energy to be an
integral multiple of a constant(h) times the
frequency.
• In other words the energy is quantized.
• En=nhf
n=0,1,2,3,…
Photoelectric effect
Energy of a photon
E  hf
h  Planck ' s constant  6.63 10 J s
-34
Figure 30-5
The Photoelectric Effect
Photoelectric effect
A photoelectron is an electron emitted through the photoelectric effect.
The maximum kinetic energy of a photoelectron K max  E - Wo
where
E is the energy given to the electron by the beam of light
Wo is the minimum amount of energy needed to ejact an electron
from a particular metal. (Called the work function).
Photoelectric effect
The cutoff (threshhold ) frequency f o is the smallest frequency that will allow
electrons to be emitted from a particular metal
Wo
fo 
h
Figure 30-6
The Kinetic Energy of Photoelectrons
Compton effect
• MC 1 and 3 page 351 (Barrons)
• FR 1(a), and 2 on page 354. (Barrons)
Matter waves
• When an x-ray photon strikes an electron,
both are scattered in a way that is consistent
with the law of conservation of momentum
(Compton effect).
• This implies that the photon has a momentum
even though it has no rest mass.
momentum of a proton
p=
h

Matter waves
• When x-rays are scattered by a crystal, the
resulting pattern is similar to that of scattered
particles.
• This implies that photons can behave like
particles.
Matter waves
• If a beam of X-rays interacts with a crystal a
pattern that looks like scattered particles.
Matter waves
• When a beam of electrons goes through two
slits, a diffraction pattern similar to the
diffraction of light results.
• This implies that particles can have a
wavelength.
Figure 30-14
Creation of an Interference Pattern
by Electrons Passing Through Two Slits
Matter waves
Wavelength of a particle
h

p
Atomic structure
• Rutherford’s group
performed the famous gold
foil experiment and found
that an atom appears to be
mostly empty space.
Atomic Structure
Atomic structure
• He proposed a “solar
system” of the atom.
Atomic structure
• When gases at low pressures
are excited, they do not
produce a typical blackbody
radiation curve, but rather
individual lines of different
colored light.
Figure 31-3
The Line Spectrum of an Atom
Figure 31-4
The Line Spectrum of Hydrogen
Atomic structure
• Johann Jakob Ballmer used
trial and error methods to
provide a simple formula that
gives the wavelengths of the
visible part of the hydrogen
spectrum.
Atomic structure
 1 1 
 R  2  2  n  3, 4,5,.......

2 n 
7
1
R  1.097 10 m
1
Atomic structure
• This was the first step in
developing a quantitative
understanding of the
hydrogen spectrum.
Bohr model
He postulated that there are
certain allowable orbits for
an electron around the
nucleus in which no loss of
energy occurs.
Energy levels for Bohr's atom
2 mk e Z
En 
2 2
hn
Bohr radius
2
2
2 4
2
hn
rn  2
2
4 mke
2
Problems
Problems 5-9 and 11-14 on
page 1046 in Walker.
Quantum Mechanics and Electron
Configurations
Review- Bohr’s model of atom and electrons

there were orbits associated with fixed energy levels that electrons could
occupy around nucleus.
The lowest energy level was closest to nucleus. When all electrons were in lowest
available energy levels the atom was in the “ground state”.
 By absorbing energy, electron could “jump” to a higher orbit or energy level. This
was called the “excited state”
When electron fell back to ground state it would emit the energy that it had
absorbed as a photon.
Quantum Mechanics and Electron
Configurations
Bohr’s model could not predict energy
levels in atoms with more than one
electron.
•1926- Erwin Schrödinger- used mathematics to
describe the behavior of electrons in atoms. He
assumed that electrons behaved like standing
waves.This is called the quantum mechanical
model. A standing wave is a wave that meets
itself without any overlap.
1927 - Heisenberg Uncertainty Principle it is
impossible to know both the precise location and
the precise velocity of a subatomic particle at the
same time
Quantum mechanics restricts the
energy of electrons to certain levels,
but unlike Bohr’s model it does not
describe an exact path the electron
takes around the nucleus.
Instead it predicts probabilities of
finding electrons in certain regions of
space
(Not in outer space, but in tiny region
of space around the nucleus)
The quantum mechanical model
determines the energy an electron can
have and how likely one is to find the
electron in various locations around
the nucleus
Just like the blur of the propeller, the probability
of finding an electron within a certain volume of
space surrounding the nucleus can be
represented as a fuzzy cloud.
The cloud is more dense where the probability
of finding an electron is high.
The quantum mechanical model is sometimes
called the charge cloud model.
The region of highest probability for each different energy level is a
plot of points. The average position of the points can be shown as a
spherical shell centered on the nucleus.
This shell or energy level is just the average of points on a
probability plot, not a path of movement of the electron.
These energy levels or shells are called
principal energy levels and they are
numbered 1,2,3 etc…..
The number of the shell or principal energy level
is called the PRINCIPAL QUANTUM NUMBER
and it is represented by the symbol n
The principal energy levels are the regions in
space that can be occupied by an electron
Every principal
energy level has
one or more
sublevels within it
The energy of
each sublevel
within the
principal level is
different
Important stuff
1. The number of
sublevels in any
principal level is the
same as its principal
quantum number
n.
So the first principal
energy level (n = 1)
has one sublevel
The 2nd principal level (n= 2) has 2
sublevels and 3rd principal level (n=3)
has 3 sublevels and so on.
Each electron in a
given sublevel has the
same energy
The lowest
sublevel in each
principal level is
called the s
sublevel
In the first
principal level
it is labeled
the 1s
sublevel
In the second
principal level it
is the 2s
sublevel
The next
higher sublevel
is called the p
sublevel
There is no p
sublevel when n
= 1; this first
principal level
has only one
sublevel, the s
sublevel
The two sublevels
of the 2’nd principal
level are labeled 2s
and 2p
When n = 3, a third
sublevel appears,
called the d sublevel
When n = 4, there is a 4th
sublevel labeled f.
RECAP
The quantum mechanical model
determines the energy an electron can
have and how likely one is to find the
electron in various locations around
the nucleus
When a photon with an energy exactly
corresponding to the difference
between two energy levels is absorbed
by an atom, an electron will move
from the lower to the higher energy
level (become excited).
When an electron moves from a higher
to the energy level to a lower energy
level, a photon with an energy exactly
corresponding to the difference
between two energy levels is emitted
by the atom,
Figure 31-8
Energy-Level Diagram for the
Bohr Model of Hydrogen
Figure 31-9a
The Origin of Spectral Series in Hydrogen
Figure 31-9b
The Origin of Spectral Series in Hydrogen
Figure 31-9c
The Origin of Spectral Series in Hydrogen
Relativity
Postulates of special relativity.
1. The laws of physics are the same in all
inertial frames of reference.
2. The speed of light in a vacuum is the
same in all inertial frames of reference
independent of the motion of the source
or the receiver.
Relativity
All inertial frames move with constant
velocity (0 acceleration) relative to one
another.
Figure 29-1
Inertial Frames of Reference
Figure 29-4
The Speed of Light for Different Observers
Relativity
As an object approaches the
speed of light, according to
the theory of special
relativity time dilation
occurs.
Figure 29-5
A Stationary Light Clock
Relativity
Consider a light clock
2d
if it is stationary , to 
c
Figure 29-6
A Moving Light Clock
Relativity
If the light clock is moving ,
2d
2d

t 
2
2
2
v
c -v
c 1- 2
c
Relativity
If the light clock is moving ,
to
t 
2
v
1- 2
c
Relativity
Length contraction
2
v
L  Lo 1- 2
c
Lo  length when object is at rest (v  0);
(also referred to as the " proper length ")
L  contracted length
Relativity
Re lativistic addition of velocities.
v1  v2
v
v1v2
1 2
c
Relativity
Relativistic momentum.
mv
p
2
v
1 2
c
Relativity
Increase of mass with speed .
mo
m
2
v
1 2
c
Relativity
Relativistic energy.
E  mc
2
Relativity
Rest energy.
E0  m0 c
2
Relativity
Relativistic kinetic energy.
K=
m0c
2
2
v
1 2
c
 m0c
2
Relativity
General relativity – applies to
accelerated frames of
reference, and to gravitation.
Relativity
Principle of equivalence– all
physical experiments conducted
in a uniform gravitational field
and in an accelerated frame of
reference give identical results.
Relativity
• According to general relativity
a gravitational field will bend
light. This was proven
experimentally. (pages 970 and
971).
Relativity
• This also results in gravitational
lensing. (P 971).
Relativity
For a body of mass M to become a
black hole its radius R must equal.
2GM
R 2
c
Where G is the universal gravitational constant
and c is the speed of light
Relativity
Problems 1,2,19,31,41, and 49 on
pages 976 -978 in Walker.
(Chapter 29)
Nuclear Physics
The nucleus of an atom consists of
protons and neutrons (nucleons).
A convenient mass unit for
nucleons is the atomic mass unit
(u)
Nuclear Physics (p1051)
1u=1.660540 x10-27 kg
A proton has the mass of 1.007276u
A neutron has the mass of 1.008664u
An electron has the mass of 0.0005485799u
Table 32-1
Numbers That Characterize a Nucleus
Z
N
A
Atomic number = number of
protons in nucleus
Neutron number = number of
neutrons in nucleus
Mass number = number of
nucleons in nucleus
(#protons + #neutrons)
Nuclear Physics
The notation used for nuclei is
A
Z
X
Where X is the symbol for the
element
Nuclear Physics
For example the symbol for an
isotope of carbon with 6 protons
and 8 neutrons in the nucleus is
written
14
6
C
Nuclear Physics
Isotopes of an element
have the same number of
protons but different
numbers of neutrons in
the nucleus.
Nuclear Physics
Hydrogen
Deuterium
1
1
H
2
1
H
Nuclear Physics
The symbol for an alpha particle
(helium nucleus) is written
4
2
He
Nuclear Physics
Nuclear distances are typically
measured in fermi (fm)
1fermi=1fm=1x10-15 m
Nuclear Physics
Nuclear distances are typically
measured in fermi (fm)
1fermi=1fm=1x10-15 m
Nuclear Physics
•The strong nuclear force holds the
nuclei together.
•It only acts at distances of a
couple of fermis or less.
•It counteracts the repulsive
electrostatic force acting on the
protons
Nuclear Physics
There are three types of articles emitted during radioactive decay
-α (alpha)particle 2 protons and two neutrons bound together (a helium ion)
Nuclear Physics
- β (beta) particle -an electron or a positron (an antielectron)
is emitted
19
10
Ne  199 F + e  + e (electron neutrino)
  decay
14
6
C  147 N + e  + e (positron neutrino)
  decay
Nuclear Physics
- γ (gamma) particle: a γ photon (very high energy)
14
6

C  147 N* + e  + e (positron neutrino)  147 N +
14
7
N indicates a nucleus in the excited state 
*
 decay
Nuclear binding energy
• All stable nuclei that contain more
than one nucleon, have masses
less than that of the individual
nucleons added together.
Nuclear binding energy
• The difference in mass is due to the
energy that holds the nuclei together
called the “binding energy”
• This phenomenon is called the mass
defect m).
• Einstein’s equation E=mc2 can be
used to calculate the binding energy
of a nucleus from the mass defect.
Half life
Radioactive isotopes decay at different rates. The decay rate
is called half-life , and it is the time it takes for half of the
radioactive atoms to decay (transmute) into a new nucleus.
Uranium-238 has a half-life of 4.5 billion years . Some
elements have a half-life of less than a second!
Half life
Nuclear Fission
Fission occurs when a heavy nucleus is split into two
relatively large chunks. Fission reactions are begun by
shooting a neutron into the nucleus, which initiates
the reaction. Large amounts of energy are released as
mass converts to energy in the reaction. This is the
reaction in nuclear power plants and nuclear weapons.
Below is an example of a plutonium fission reaction.
239
94
Pu + 01 n  100
40 Zr +
137
54
Xe +3  01 n   Energy
Nuclear Fusion
Fusion occurs when two light nuclei combine to
make a new heavier and more stable nucleus.
Large amounts of energy are released in the
reaction. This is what happens in the sun and in
thermonuclear weapons. Here is an example of
fusion. Notice how one of the products of the
reaction is larger than any of the originals.
2
1
H + He  He + H +  18.3Mev
3
2
4
2
1
1
Nuclear reactions - fission