Download Chapter 27

Chapter 27
Quantum Physics
Conceptual questions: 1,3,9,10
Quick Quizzes: 1,2,3
Problems: 13,42,43,51
Problems which classical
physics could not solve

Blackbody Radiation


E&M radiation emitted by a heated object
Photoelectric Effect

Emission of electrons by an illuminated metal
X-Ray Diffraction
 The Compton Effect
 Spectral Lines Emitted by Atoms

Blackbody Radiation

An object at any temperature is known to
emit electromagnetic radiation, called
thermal radiation

Stefan’s Law, the power radiated by an object,
P = s A e T4


T-temperature, A-area, e-emissivity, s=5.669 10-8 W/m2 K4
The spectrum of the radiation depends on the
temperature and properties of the object
Blackbody Radiation Graph

The wavelength of the peak
of the blackbody
distribution was found to
follow Wein’s Displacement
Law


λmax T = 0.2898 x 10-2 m • K
λmax is the wavelength at the
curve’s peak
The Ultraviolet Catastrophe and Planck’s
theory



Classical theory predicted
infinite energy at low
wavelengths
Planck hypothesized that the
blackbody radiation was
produced by resonators
The resonators could only
have discrete energies

En = n h ƒ



n is called the quantum number
ƒ is the frequency of vibration
h is Planck’s constant, 6.626 x
10-34 J s
Photoelectric Effect



When light strikes E,
photoelectrons are
emitted
Electrons collected at C
and passing through the
ammeter are a current
in the circuit
C is maintained at a
positive potential by the
power supply
Photoelectric Current/Voltage Graph
Classical theory could
not explain:
 The stopping potential is
independent of the
radiation intensity
 The maximum kinetic
energy of the
photoelectrons is
independent of the light
intensity
 The maximum kinetic
energy of the
photoelectrons increases
with increasing light
frequency
Einstein’s Explanation






Light is a collection of photons (not waves)
The photon’s energy would be E = hƒ
E=nhf-(n-1)hf
Each photon can give all its energy to an
electron in the metal
The maximum kinetic energy of the liberated
photoelectron is KE = hƒ – Φ
Φ is called the work function of the metal
Verification of Einstein’s
Theory
Problem 27-13. What wavelength of light would have to fall on
sodium (work function 2.46 eV) if it is to emit electrons with a
maximum speed of 1.0 x 106 m/s?
Photocells
Photocells are an application of the
photoelectric effect
 When light of sufficiently high
frequency falls on the cell, a current is
produced
 Examples


Streetlights, garage door openers,
elevators
Problem 27-13

What wavelength of light would have to
fall on sodium (with a work function of
2.46 eV) if it is to emit electrons with a
maximum speed of 1.0 × 106 m/s?
X-Rays

Electromagnetic radiation with short
wavelengths
Wavelengths less than for ultraviolet
 Wavelengths are typically about 0.1 nm
 X-rays have the ability to penetrate most
materials with relative ease


Discovered and named by Roentgen in
1895
Production of X-rays
Schematic for X-ray Diffraction
A continuous beam of
X-rays is incident on
the crystal
 The diffracted
radiation is very
intense in certain
directions


These directions correspond
to constructive interference
from waves reflected from
the layers of the crystal
Diffraction pattern
for NaCl
Bragg’s Law

Bragg’s Law gives the
conditions for constructive
interference
2 d sin θ = m λ
m = 1, 2, 3…
Compton Scattering



Compton assumed the
photons acted like
other particles in
collisions
Energy and
momentum were
conserved
The shift in
wavelength is
h
     o 
(1  cos )
me c
QUICK QUIZ 27.1
An x-ray photon is scattered by an
electron. The frequency of the
scattered photon relative to that of
the incident photon
(a) increases,
(b) decreases,
(c) remains the same.
QUICK QUIZ 27.2
A photon of energy E0 strikes a free
electron, with the scattered photon of
energy E moving in the direction opposite
that of the incident photon. In this
Compton effect interaction, the resulting
kinetic energy of the electron is
(a) E0 ,
(b) E ,
(c) E0  E ,
(d) E0 + E ,
(e) none of the above.
Photons and Electromagnetic
Waves

Light has a dual nature. It exhibits
both wave and particle characteristics

Applies to all electromagnetic radiation
The photoelectric effect and Compton
scattering offer evidence for the particle
nature of light
 Interference and diffraction offer
evidence of the wave nature of light

Wave Properties of Particles

In 1924, Louis de Broglie postulated
that because photons have wave and
particle characteristics, perhaps all
forms of matter have both properties

Furthermore, the frequency and
wavelength of matter waves can be
determined
de Broglie Wavelength and
Frequency

The de Broglie wavelength of a particle
is
h

mv

The frequency of matter waves is
E
ƒ
h
QUICK QUIZ 27.3
A non-relativistic electron and a nonrelativistic proton are moving and have
the same de Broglie wavelength. Which
of the following are also the same for the
two particles:
(a) speed,
(b) kinetic energy,
(c) momentum,
(d) frequency?
The Electron Microscope



The electron microscope
depends on the wave
characteristics of electrons
Microscopes can only resolve
details that are slightly
smaller than the wavelength
of the radiation used to
illuminate the object
The electrons can be
accelerated to high energies
and have small wavelengths
The Uncertainty Principle

When measurements are made, the
experimenter is always faced with
experimental uncertainties in the
measurements


Classical mechanics would allow for
measurements with arbitrarily small
uncertainties
Quantum mechanics predicts that a
barrier to measurements with ultimately
small uncertainties does exist
Heisenberg’s Uncertainty
Principle

Mathematically, xp x  h
4

It is physically impossible to measure
simultaneously the exact position and
the exact linear momentum of a particle

Another form of the principle deals with
energy and time:
h
Et 
4
Problem 27-43

In the ground state of hydrogen, the
uncertainty of the position of the
electron is roughly 0.10 nm. If the
speed of the electron is on the order of
the uncertainty in its speed, how fast is
the electron moving?
Thought Experiment – the Uncertainty
Principle




A thought experiment for viewing an electron with a powerful
microscope
In order to see the electron, at least one photon must bounce
off it
During this interaction, momentum is transferred from the
photon to the electron
Therefore, the light that allows you to accurately locate the
electron changes the momentum of the electron
Scanning Tunneling
Microscope (STM)
Allows highly detailed
images with resolution
comparable to the size
of a single atom
 A conducting probe with
a sharp tip is brought
near the surface
 The electrons can
“tunnel” across the
barrier of empty space

Conceptual questions
1. If you observe objects inside a very hot kiln, it
is difficult to discern the shapes of the objects.
Why?
 3. Are the blackbodies really black?
 9. In the photoelectric effect, explain why the
stopping potential depends on the frequency of
the light but not on the intensity.
 10. Which has more energy, a photon of
ultraviolet radiation or a photon of yellow light?

Problems
42. A 50-g ball moves at 30.0 m/s. If its
speed is measured to an accuracy of 0.10%,
what is the minimum uncertainty in its
position?
 51. Photons of wavelength 450 nm are
incident on a metal. The most energetic
electrons ejected from the metal are bent into
a circular arc of radius 20.0 cm by a magnetic
field with a magnitude of 2.00 × 10–5 T. What
is the work function of the metal?
