Transcript Early Quantum Theory and Models of the Atom

Early Quantum Theory
AP Physics
Chapter 27
Early Quantum Theory
27.1 Discovery and Properties of
the Electron
27.1 Discovery and Properties of the Electron
Glass tube filled with
a small amount of
gas
When a large voltage
was applied
A dark shape
seemed to
extend from
the cathode
27.1
27.1 Discovery and Properties of the Electron
Name Cathode Rays
Deflected by electric or magnetic fields
Negative charge
JJ Thompson – discovered the electron
Believed that the electron was
a part of the atom
Robert Millikan – determined
the charge on an electron
Experiment Video
27.1
Early Quantum Theory
27.2 Planck’s Quantum
Hypothesis
27.2 Planck’s Quantum Hypothesis
Blackbody Radiation – all objects emit
radiation proportional to T4 (in Kelvin)
Normal Temp – low intensity
Above 300K – we can sense
the IR as heat
At about 1000K objects glow
Above 2000K glow yellow
-white
27.2
27.2 Planck’s Quantum Hypothesis
As temperature increases
EMR emitted increases
increases toward higher frequencies
27.2
27.2 Planck’s Quantum Hypothesis
Blackbody – absorbs all the radiation that falls
on it
Blackbody radiation – the EMR that a
blackbody emits when hot and lumnous
Max Plank (1900) – purposed
his Quantum Hypothesis
Energy of any molecular vibration
could only be a whole number
multiple of a minimum value
E  hf
27.2
27.2 Planck’s Quantum Hypothesis
E  hf
h is called Planck’s constant
h  6.626 x10
34
J s
Since energy has to be a whole number
multiple
E  nhf
n – is a quantum number
It is quantized – occurs in only discrete
quantities
27.2
S-149
What do the following terms mean
A. Quantized
B. Discrete Energy Levels
C. E=mc2
S-150
How much energy is released by the alpha
decay of Uranium 238?
How much energy would be created by a
sample 100g of pure U-238 if the half life is
4.468x109 years.
(molar mass of Thorium-234=234.0436u)
Early Quantum Theory
27.3 Photon Theory of Light and
the Photoelectric Effect
27.3 Photon Theory of Light
Einstein (1905) – when an object
emits light its energy must be
decreased by hf, so light is
emitted in quanta where
E  hf
Where f is the frequency of
the quanta emitted
Light is transmitted as tiny
particles called photons
27.3
27.3 Photon Theory of Light
When light shines on metals – electrons are
emitted from the surface
Called the photoelectric effect
Both photon theory and wave
theory are consistent with
this basic result
27.3
27.3 Photon Theory of Light
Wave theory predicts (for monochromatic
light)
1. Increased light intensity should
a. Increase the number of electrons
ejected
b. The maximum kinetic energy of the
should be higher
2. Frequency of light should not affect kinetic
energy, only the intensity
27.3
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic
light)
All photons of the same frequency would have
the same energy
E  hf
All the energy of a photon would be
transferred to an electron
Since electrons are held in the metal by some
force, a minimum energy must be reached
before an electron can be emitted
27.3
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic
light)
This minimum energy is called the work
function (W0)
Electrons that absorb less than W0 will not be
ejected
Those that are ejected the energy will be
hf  KE  W
For the least tightly held electrons
hf  KEmax  W0
27.3
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic
light)
1. Increase in intensity will result in
a. More electrons being ejected
b. The same maximum kinetic energy for
all the electrons
2. If frequency is increased, the maximum
kinetic energy increase linearly
KEmax  hf  W0
27.3
27.3 Photon Theory of Light
Photon theory predicts (for monochromatic
light)
3. Below a cutoff frequency no electrons will
be ejected
hf  W0
Experiments have proven that emitted
electrons follow the photon theory
27.3
S-149
A sheet of metal has a work function of
5.6x10-17 J. What is the minimum
frequency of photons that will cause
electrons to be ejected?
Early Quantum Theory
27.4 Energy, Mass, and
Momentum of a Photon
27.4 Mass, Energy, and Momentum of a Photon
The momentum of a particle at rest is given by
p
m0v
1
v2
c2
(from relativity chapter)
Since a photon travels at c, either it has
infinite momentum, or its rest mass is 0
(makes sense, the photon is never at rest)
The energy of a photon is KE  E  hf
27.4
27.4 Mass, Energy, and Momentum of a Photon
The momentum of a photon is developed from
the relativistic formula
E  p c m c
2
Since m0=0
Usually written
2 2
2 4
0
EE  ppcc
2
2 2
hf h
p

c 
27.4
S-151
A photon with a wavelength of 620 nm is shot
at a metal surface.
A. What is the frequency of the photon?
B. What is the energy of the photon?
C. If the result is an electron being ejected
with a kinetic energy
of 1.2 x 10-19 J, what
is the work function
of the metal?
Early Quantum Theory
27.6 Photon Interactions; Pair
Production
27.6 Photon Interaction, Pair Production
Four interactions that photons undergo atoms
1. Photoelectric effect
2. Move an electron to
an excited state
3. Photon can be scattered
resulting in lower frequency
(energy) photon – called
the Compton Effect
27.6
27.6 Photon Interaction, Pair Production
Four interactions that photons undergo atoms
4. Pair production – a photon creates matter
The photon disappears and produces a
electron-positron pair
Example of mass being
produced in accord with
E  mc
2
The positron will quickly
collide with an electron
27.6
27.6 Photon Interaction, Pair Production
Pair production must occur near a nucleus so
that momentum can be conserved
Used in PET scanners (positron emission
tomography)
27.6
Early Quantum Theory
27.7 Wave-Particle Duality
27.7 Wave-Particle Duality
Light properties can sometimes only be
explained using particle theory (photons)
Sometimes the properties can only be
explained using wave theory.
This realization that light has both properties
is called wave-particle duality
The principle of complementarity – to fully
understand light, we must be aware of
both its particle and its wave natures
27.7
Early Quantum Theory
27.8 Wave Nature of Light
27.8 Wave Nature of Matter
Louis de Broglie (1923) – proposed
all particles have wave
properties
The wavelength of a particle
is related to is momentum
h
p 
p
This is called the de Broglie wavelength
27.8
27.8 Wave Nature of Matter
The wavelength of a 0.20kg ball traveling at
15 m/s would be
34
6.6 x10 J sh
34


 2.2 x10 m
ps)
(0.20kg)(15m /mv
This is ridiculously small
Interference and diffraction only occur if a slit
is not much larger than the wavelength
So the wave properties of ordinary objects is
not detectable
27.8
27.8 Wave Nature of Matter
But atomic particles have small enough
masses that their de Broglie wavelength is
measureable
This is the
diffraction
pattern of an
electron
27.8
S-150
What is the deBroglie wavelength of a 122 kg
cat running at 9% of light speed? (He is
very fast)
Early Quantum Theory
27.10 Early Models of the Atom
27.10 Early Models of the Atom
Plum Pudding Model (1890)
JJ Thomson – homogeneous sphere of
positive charge embedded with negative
electrons
27.10
27.10 Early Models of the Atom
Planetary Model (1911) Ernest Rutherford
Tiny positively charged nucleus contains most
of the mass
Electrons orbit around the nucleus like planets
around the sun
27.10
Early Quantum Theory
27.11 Atomic Spectra: key to the
Structure of the Atom
27.11 Atomic Spectra
If a pure gas in a tube is
excited
It produces a discrete
spectrum
When looked at through a
spectrometer we can observe a emission
spectrum unique to that element
If a continuous spectrum passes through a
gas, dark lines, or an absorption spectrum,
is visible
27.11
27.11 Atomic Spectra
It is assumed that in low density gases, the
spectrum is from individual atoms
Hydrogen is the simplest atom, and shows a
regular pattern to its spectral lines
JJ Balmer – showed that four lines in the
visible spectrum of hydrogen have
wavelength that fit the formula
 1 1 
 R 2  2 

2 n 
1
27.11
27.11 Atomic Spectra
R is called the Rydberg Constant
n = the integer values starting with 3
Later, the Lyman series was found to fit
Paschen series
1 1 
 R 22  22 

 312 n 
1
27.11
S-152
Which, if any, of the following changes in
electron energy state will result in a photon
of visible light (=700nm to =400nm)?
Early Quantum Theory
27.12 The Bohr Model
27.12 Bohr Model
Niels Bohr – electrons cannot lose
energy continuously, but in
quantum jumps
Light is emitted when an electron
jumps from a higher state to
a lower state
hf  Eu  El
He compared a quantized angular momentum
to the Balmer series
27.12
27.12 Bohr Model
Although the results worked
h
v
LL
mvr
LL

(mr
)(
nI n r )
2
2
n is an integer called the principle quantum
number
It was simply chosen because it
worked
The lowest E1 – ground state
Higher levels – excited state
27.12
27.12 Bohr Model
The minimum energy level required to remove
an electron from the ground state is called
the ionization energy
For hydrogen is it 13.6eV and precisely
corresponds to the energy to go from E1 to
E=0
Often shown in an Energy Level Diagram
Vertical arrows show transitions
Energy released or absorvedcan be
calculated by the difference between
27.12
energy at each level
Early Quantum Theory
27.13 de Broglie’s Hypothesis
Applied to Atoms
27.13 de Broglie’s Hypothesis Applied to Atoms
Bohr could give no reason why electrons were
quantized
Reason was purposed by de Broglie
A particle of mass moving with a
h
nonrelativistic speed would have  
mv
a wavelength such that
If each electron orbit is treated as a standing
wave we get
h
This is the quantum condition
mvrn  n
purposed by Bohr
2
27.13
S-153
Last Test Day!!
S-153
A pig is shot with an initial velocity of
25m/s @ 52o.
A. What is the maximum height reached?
B. How far from the canon does he land?
S-154
A 9.2 kg cat is slid across a table with a
coefficient of friction of 0.2. The initial
velocity of the cat is 31 m/s, and the
table is 15 m long and 5 m tall.
A. What is the velocity of
the cat at the end of the
table?
B. What is the velocity of
the cat as it hits the
ground?
S-155
A 600 kg cow is spun horizontally on a 5.00
m string. If the maximum tension on
the string can be 10,000 N, how fast can
he spin without breaking the string?
S-156
The mass above is 3.7 kg. The angle is 28o.
What is the tension in each string?
Random hamster
S-157
A 25g bullet is shot at 200 m/s into a
pendulum that has a mass of 1.5 kg and
a length of 2.6 m. What is the maximum
angle with the vertical that the
pendulum will
make if the bullet
lodges into the
bob?
S-158
A car enters a curve with a radius of 12.9m.
The coefficient of friction between the
car and the road is 0.311. What is the
maximum velocity that the car can
travel at while in the curve?
S-160
Solve the following torque problem
Mg=1.4 N
mg=3.5 N
L=0.62m
d=0.05m
What is the force of
the bicep?
S-161
Two electrons are placed 0.000045 cm from
each other.
A. What is the force between them?
B. What is the electric field at that distance
from one of the electrons?
C. What is the electric potential energy of one
electron?
D. What is the potential difference at that
distance from one of them?
S-162
An electron is accelerated through a 12 V
field.
A. What is it’s velocity?
B. It is how shot (right to left) into a 4.5 T field
that is directed upward. What is the force
on the electron (magnitude and direction)?
C. It travels in a curved
path, what is the radius
of the path?
S-163
A 150g chunk of Smellium – 352 is measured
to have a half life of 3.8s.
A. What is the decay constant?
B. What is the decay rate?
S-165
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