Download Origin of Quantum Theory

Origin of Quantum Theory
Black Body Radiation
Photoelectric Effect
Compton Scattering
Origins of Quantum Theory
Who first postulated the idea of light quanta?
1. Planck
2. Bohr
3. De Broglie
4. Einstein
5. Heisenberg
Origins of Quantum Theory
Who first postulated the idea of light quanta?
1. Planck
2. Bohr
3. De Broglie
4. Einstein
5. Heisenberg
Origins of Quantum Theory
In the photoelectric effect experiment, current
flows when the light frequency is
1. less then the threshold frequency.
2. equal to the threshold frequency.
3. greater then the threshold frequency.
4. less than the cathode’s work function.
5. equal to the cathode’s work function.
Origins of Quantum Theory
In the photoelectric effect experiment, current
flows when the light frequency is
1. less then the threshold frequency.
2. equal to the threshold frequency.
3. greater then the threshold frequency.
4. less than the cathode’s work function.
5. equal to the cathode’s work function.
Origins of Quantum Theory
The minimum amount of energy needed to free an
electron from a piece of metal is called the
1. Gibb’s free energy.
2. quantum energy.
3. liberation potential.
4. threshold energy.
5. work function.
Origins of Quantum Theory
The minimum amount of energy needed to free an
electron from a piece of metal is called the
1. Gibb’s free energy.
2. quantum energy.
3. liberation potential.
4. threshold energy.
5. work function.
Origins of Quantum Theory
Blackbody Radiation
Planck
(1900)
En = nhf
Compton scattering
Compton
(1923)
Photoelectric Effect
A. Einstein
(1905)
Bohr Atom
N. Bohr
(1911)
Origins of Quantum Theory

Introduction to Radiation
Hot Solid
Hot Gas
Cold Gas
Origins of Quantum Theory

Spectra
Absorption spectra
Emission or Line spectra
Origins of Quantum Theory

This is one way we identify interstellar elements.
Origins of Quantum Theory

Blackbody Radiation
What happens when you turn on the electric bunner on a stove?


Demonstration - light bulb filament
Demonstration - idea blackbody
Origins of Quantum Theory

How was the spectra measured?
Origins of Quantum Theory

Here is what they knew at the turn of the century.

The total power radiated is
Pblackbody  AT
  5.67X108 W m 2K 4
4
P
I
A
power
area
The wavelength for maximum radiation is inversely
 proportional to the temperature
area under curve
  T  2.898X103 mK

max


The distribution of wavelengths depends
on the temperature only, not the material.
R,T 
Origins of Quantum Theory
T = ________
7,000 K
max = ________
425 nm
max T = ________
3.0X10-3 mK
T = ________
6,000 K
485 nm
max = ________
max T = ________
3.0X10-3 mK
T = ________
5,000 K
max = ________
600 nm
max T = ________
3.0X10-3 mK
What do you notice about these values?
They all have the same value.
max T  2.898X103 mK
Origins of Quantum Theory
Origins of Quantum Theory

Classical Theory (Maxwell’s Electromagnetic Theory)
R( ,T) 

2ckT

ultraviolet catastrophe
4
Planck’s Theory (Quanta)
E  nhf
2hc
R( , T )  5 hc kT
 e
 1
2

Origins of Quantum Theory

Photoelectric Effect
Origins of Quantum Theory
E before  E after
hf  E0  KEe
E0 is the work function or binding energy
KEe  eVstopping
E0 h
Vstopping  
 f
e e
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
Origins of Quantum Theory
The work function of metal A is 3.0 eV. Metals B and C have
work functions of 4.0 eV and 5.0 eV, respectively. Ultraviolet
light shines on all three metals, creating photoelectrons. Rank
in order, from largest to smallest, the stopping voltages for A,
B, and C.
1. VA > VB > VC
2. VC > VB > VA
3. VA = VB = VC
Origins of Quantum Theory
The work function of metal A is 3.0 eV. Metals B and C have
work functions of 4.0 eV and 5.0 eV, respectively. Ultraviolet
light shines on all three metals, creating photoelectrons. Rank
in order, from largest to smallest, the stopping voltages for A,
B, and C.
1. VA > VB > VC
2. VC > VB > VA
3. VA = VB = VC
Origins of Quantum Theory
The intensity of a beam of light is increased but the light’s
frequency is unchanged. Which of the following is true?
1. The photons travel faster.
2. Each photon has more energy.
3. There are more photons per second.
4. The photons are larger.
Origins of Quantum Theory
The intensity of a beam of light is increased but the light’s
frequency is unchanged. Which of the following is true?
1. The photons travel faster.
2. Each photon has more energy.
3. There are more photons per second.
4. The photons are larger.
Origins of Quantum Theory

Compton Scattering
scattered
incident


h
  scattered  incident 
1 cos 
mc
Origins of Quantum Theory

Compton Scattering
h
  scattered  incident 
1 cos 
mc
Origins of Quantum Theory

Classical Scattering of Electromagnetic Wave
We do not have to consider the magnetic field
since it is so small compared to the electric field
So the radiation wavelength is the
same as the incident wavelength.
Origins of Quantum Theory



Compton Scattering
Answer the first three questions in the tutorial and draw the
diagram for the scattering experiment.
Discuss the Compton experiment in your group. What are the
two physical quantities in the collision?
What is the assumption for light that Compton used?
That light behaved like a particle with energy
E  hf
And momentum

E hf
p 
c
c
E 
2
pc 
2
 mc

2 2
 m  0
Origins of Quantum Theory

Compton Scattering

What two equations (conservation law) did Compton use to
find the change in wavelength?
Conservation of energy
Conservation of momentum

Draw the collision between the electron and the photon. Label
the angles  and .
Origins of Quantum Theory
Write the energy and momentum for each before and after the
collision
Conservation of Energy

E p ,i  Ee ,i  E p , f  Ee , f
hfi  me c  hf f 
2
Conservation of Momentum
 p c   mc 
2 2
2
e

pp, f




p p ,i  p p , f  pe
p
2
2
2
pe  p p ,i  p p , f  2 p p ,i p p , f cos 
p ,i

pe
Origins of Quantum Theory
Write the energy and momentum for each before and after the
collision
before
after
electron
E e, f  ?
E  m c2

e,i
pe,i  0
e
pe, f 
Ee  mec
2

2 2
photon h
1 cos 
mc
E p, f  hf
f
  scattered  incident 

E p,i  hfi


E p ,i hfi h


p p,i 
c
c i


p p, f
E p , f hf f
h



c
c f
Origins of Quantum Theory
Origins of Quantum Theory

Introduction to Radiation
Solid
Hot Gas
Cold Gas
Origins of Quantum Theory

Planck’s Theory (Quanta)
2hc 2
R( ,T)  5 hc kT 1
 e

 
2hc 2
R( , T )  5 hc kT

 e
 1
2hc 2
2hc 2 kT 2c


 4 kT
5
hc

hc


5
 1 
   1
 kT

Classical expression
Origins of Quantum Theory

Planck’s Theory (Quanta)
2hc 2
R( ,T)  5 hc kT 1
 e

 0
2hc 2
R( , T )  5 hc kT

 e
 1
2hc 2 2hc 2  hc kT
 5 hc kT 
e
5
e

Origins of Quantum Theory

Optical Pyrometer
Origins of Quantum Theory

Microwave Cosmic Background
Origins of Quantum Theory
Origins of Quantum Theory

Use the results above and substitute into the conservation
equation.

Do the same for conservation of momentum in the x direction.

Now for momentum in the y direction.

Compton solved these three equations to find =  - .
Where  is the initial wavelength for the photon and  is the
final wavelength for the photon.

What is the final results (Compton’s equation) that Compton
found?
h
  scattered  incident 
1 cos 
mc