Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
Early Quantum Theory and Models of the Atom
Sections 27.1 - 27.3
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Reading Assignment
Read section 27.4 - 27.8
Homework Assignment 11
Homework for Chapter 26 is due in class today
Homework Assignment 12
Homework for Chapter 27 (due at the beginning of class on Friday, November 19)
Q: 2, 7, 14, 20, 28
P: 12, 24, 38, 44, 48, 56
Early Quantum Theory and Models of the Atom
Final Questions
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
A brief history of quantum mechanics
1900: In order to explain black body radiation, Max Planck proposes that electromagnetic energy is
quantized
1905: Using Planck’s hypothesis (that light consisted of individual quantum particles), Albert Einstein
explains the mysterious photoelectric effect
1913: Niels Bohr proposes a new model for the hydrogen atom (the Bohr model), where negatively
charged electrons are only allowed to revolve around the nucleus at fixed (quantized) distances; he
hypothesizes that these electrons can transition from one orbit to another, emitting or absorbing a
particular amount of energy in the process
1922: Otto Stern and Walther Gerlach detect discrete values of angular momentum for atoms
1924: Louis de Broglie proposes that matter has wave properties (de Broglie wavelength)
1925: Wolfgang Pauli formulates the Pauli exclusion principle
1926: Erwin Schrödinger uses de Broglie’s electron wave postulate to develop the “wave equation”
1927: Werner Heisenberg formulates the uncertainty principle
1927-1928: Development of the Copenhagen interpretation
1940s: Formulation of quantum electrodynamics (the study of how light and matter interact)
1948: Richard Feynman develops the path integral formulation of quantum mechanics
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Block body
A black body is an object that absorbs all electromagnetic radiation that falls on it
No electromagnetic radiation passes through a black body, and none is reflected
A black body object appears black when it is cold
Black bodies are the best absorbers of light and the best emitters of light
Early Quantum Theory and Models of the Atom
Final Questions
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
Block body
A black body is an object that absorbs all electromagnetic radiation that falls on it
No electromagnetic radiation passes through a black body, and none is reflected
A black body object appears black when it is cold
Black bodies are the best absorbers of light and the best emitters of light
Thermal radiation
Thermal radiation is electromagnetic radiation emitted from the surface of an object due to the object’s
temperature
The distribution of wavelengths emitted by an object depends upon
the object’s emissivity
the object’s temperature
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
Block body
A black body is an object that absorbs all electromagnetic radiation that falls on it
No electromagnetic radiation passes through a black body, and none is reflected
A black body object appears black when it is cold
Black bodies are the best absorbers of light and the best emitters of light
Thermal radiation
Thermal radiation is electromagnetic radiation emitted from the surface of an object due to the object’s
temperature
The distribution of wavelengths emitted by an object depends upon
the object’s emissivity
the object’s temperature
Emissivity
Emissivity is the measure of a surface’s capacity to emit or absorb thermal radiation, relative to that of a
perfectly black object at the same temperature
It is a dimensionless number between 0 and 1
The emissivity of a perfectly black object is 1 (black body)
The emissivity of a perfectly shiny surface is 0
The emissivity of human skin is about 0.70
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Stefan-Boltzmann law
The power radiated by an object due to its temperature depends upon its emissivity and its temperature
P =·σ·A·T
4
Wien’s law
The wavelength λmax at the peak of the spectrum is
λmax =
b
T
What are these things?
P: the total power radiated by the object
: the emissivity of the object
σ: the Stefan-Boltzmann constant, σ = 5.67 × 10−8 J/(s · m2 · K4 )
A: the surface area of the object
T : the temperature of the object (in Kelvin)
b: Wien’s displacement constant, b = 2.90 × 10−3 m·K
Early Quantum Theory and Models of the Atom
Final Questions
Announcements
Blackbody Radiation
Early Quantum Theory and Models of the Atom
The Photoelectric Effect
Final Questions
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
Planck’s hypothesis
In 1900, while working on the problem of blackbody radiation (and trying to improve upon Wien’s law),
Max Planck proposed that the energy of the oscillations of atoms in molecules was quantized (only came in
discrete amounts, or lumps)
Planck assumed that the energy of any molecular vibration could only be
E = nhf ,
n = 1, 2, 3, . . . ,
where n is called a quantum number and h is Planck’s constant
h = 6.63 × 10
−34
J·s
With this assumption, Planck was able to derive a function (Planck’s function) that fit the data for
blackbody radiation remarkably well
Even so, Planck did not attribute any physical significance to his assumption
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Around this time, scientists were puzzled by an experiment whose results seemed at odds with Maxwell’s
wave theory of light
When light shines on a metal surface, electrons are emitted; this effect is called the photoelectric effect
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Around this time, scientists were puzzled by an experiment whose results seemed at odds with Maxwell’s
wave theory of light
When light shines on a metal surface, electrons are emitted; this effect is called the photoelectric effect
From Maxwell’s wave theory of light, scientists predicted that:
Changing the frequency of the light should have no affect on the kinetic energy of the ejected
electrons
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Around this time, scientists were puzzled by an experiment whose results seemed at odds with Maxwell’s
wave theory of light
When light shines on a metal surface, electrons are emitted; this effect is called the photoelectric effect
From Maxwell’s wave theory of light, scientists predicted that:
Changing the frequency of the light should have no affect on the kinetic energy of the ejected
electrons
Increasing the intensity of the light should increase both the number and energies of ejected
electrons (why? )
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Around this time, scientists were puzzled by an experiment whose results seemed at odds with Maxwell’s
wave theory of light
When light shines on a metal surface, electrons are emitted; this effect is called the photoelectric effect
From Maxwell’s wave theory of light, scientists predicted that:
Changing the frequency of the light should have no affect on the kinetic energy of the ejected
electrons
Increasing the intensity of the light should increase both the number and energies of ejected
electrons (why? )
Instead, scientists found that:
Increasing the frequency of the light increased the maximum kinetic energy of the ejected electrons
(Philipp Lénárd, in 1902)
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Around this time, scientists were puzzled by an experiment whose results seemed at odds with Maxwell’s
wave theory of light
When light shines on a metal surface, electrons are emitted; this effect is called the photoelectric effect
From Maxwell’s wave theory of light, scientists predicted that:
Changing the frequency of the light should have no affect on the kinetic energy of the ejected
electrons
Increasing the intensity of the light should increase both the number and energies of ejected
electrons (why? )
Instead, scientists found that:
Increasing the frequency of the light increased the maximum kinetic energy of the ejected electrons
(Philipp Lénárd, in 1902)
In 1905 (the “Miracle Year”), Albert Einstein applied Planck’s quantum hypothesis to solve this apparent
paradox
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Einstein proposed a property of electromagnetic radiation that is not predicted by Maxwell’s equations:
when an atom emits or absorbs light, energy is transferred in small, discrete lumps of energy
These lumps of energy are now called photons
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Einstein proposed a property of electromagnetic radiation that is not predicted by Maxwell’s equations:
when an atom emits or absorbs light, energy is transferred in small, discrete lumps of energy
These lumps of energy are now called photons
According to Einstein’s proposal, the energy E transferred by a single photon associated with a light wave
of frequency f is
E = hf
where h is Planck’s constant
The Planck constant h = 6.63 × 10−34 J·s is the basic constant of quantum mechanics
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
The photoelectric effect
Einstein proposed a property of electromagnetic radiation that is not predicted by Maxwell’s equations:
when an atom emits or absorbs light, energy is transferred in small, discrete lumps of energy
These lumps of energy are now called photons
According to Einstein’s proposal, the energy E transferred by a single photon associated with a light wave
of frequency f is
E = hf
where h is Planck’s constant
The Planck constant h = 6.63 × 10−34 J·s is the basic constant of quantum mechanics
From this assumption, Einstein found (from conservation of energy) that
hf = Kmax + ϕ,
where Kmax is the maximum kinetic energy of an ejected electron
To just escape from the target, an electron must pick up a minimum energy ϕ, where ϕ is a property of
the target material called its work function
Note that the photoelectric effect does not occur if the frequency is less than a certain cutoff frequency f0 ,
no matter how intense the light is
Early Quantum Theory and Models of the Atom
Announcements
Blackbody Radiation
The Photoelectric Effect
Scenario
The work function of tungsten is 4.50 eV. (Recall that 1 eV = 1.6 × 10−19 J.)
Early Quantum Theory and Models of the Atom
Final Questions
Announcements
Blackbody Radiation
The Photoelectric Effect
Scenario
The work function of tungsten is 4.50 eV. (Recall that 1 eV = 1.6 × 10−19 J.)
Question
What is the cutoff frequency f0 for tungsten?
Early Quantum Theory and Models of the Atom
Final Questions
Announcements
Blackbody Radiation
The Photoelectric Effect
Final Questions
Scenario
The work function of tungsten is 4.50 eV. (Recall that 1 eV = 1.6 × 10−19 J.)
Question
What is the cutoff frequency f0 for tungsten?
Answer
The photoelectric effect does not occur below the cutoff frequency, so at the cutoff frequency we assume
that Kmax = 0
Therefore, using Einstein’s equation for the photoelectric effect, and solving for f0 , we find that
f0 =
ϕ
h
(4.50 eV)(1.6 × 10−19 J/eV)
=
15
= 1.09 × 10
6.63 × 10−34 J · s
Hz
This frequency corresponds to a wavelength of
λ0 =
c
f0
=
which is in the ultraviolet spectrum
Early Quantum Theory and Models of the Atom
3 × 108 m/s
1.09 × 1015 Hz
= 2.75 × 10
−7
m = 275 nm,
Announcements
Blackbody Radiation
The Photoelectric Effect
Reading Assignment
Read section 27.4 - 27.8
Homework Assignment 11
Homework for Chapter 26 is due in class today
Homework Assignment 12
Homework for Chapter 27 (due at the beginning of class on Friday, November 19)
Q: 2, 7, 14, 20, 28
P: 12, 24, 38, 44, 48, 56
Early Quantum Theory and Models of the Atom
Final Questions