Transcript 近代科學發展

近代科學發展
近代物理學發展
To understand a science it is
necessary to know its history.
----AUGUST COMTE
Content
Class I: 歷史 & 相對性原理
 Class II: Quantum Theory(量子論)
 Class III: Statistic Physics(統計物理)
 Class IV: Semiconductor Theory(半導體)
 Class V: Atomic Physics(原子物理)
 Class VI: Elementary Particles and
Modern Cosmology(基本粒子與近代天文
學)

History -1
1895為古典物理與近代物理分界點.
 1895以前, 人們以為: 重力, 電, 磁等已被
全然了解.
 1895以後, 其他的作用力如核力與若作用
力陸續被發現.

Classical Physics of the 1890s
Scientists could easily access political
leader.
 Basic research was recognized helpful.
 Scientists felt that given enough time and
resources, they could explain just about
anything.
 They didn’t clearly understand the
structure of matter.

Classical Physics of the 1890s

Classical ideas of physics:
Conservation of Energy
 Conservation of Linear Momentum
 Conservation of Angular Momentum
 Conservation of Charge


These conservation laws are reflected in
the laws of mechanics,
electromagnetism, and thermodynamics.
Classical Physics of the 1890s
Electricity and magnetism had been
combined by the great James Clerk
Maxwell (1831-1879) in his four
equations.
 Optics had been shown by Maxwell,
among others, to be a special case of
electromagnetism.
 Waves were believed an important
component of nature.

Mechanics

The laws of mechanics were developed
over hundreds of years by many
researchers, most astronomers.
 Galileo (1564-1642) may be called the first
great experimenter.
 His experiments ad observations laid the
groundwork for the important discoveries to
follow during the next two hundred years.
Mechanics

Isaac Newton (1642-1727) was certainly the
greatest scientist of his name and one the best
the world has ever seen.
 His discoveries were in the fields of
mathematics, astronomy, and physics and
include gravitation, optics, motion, and forces.
 He also spent considerable time on alchemy
and theology.
Mechanics

He clearly understood the relationships among
position, displacement, velocity, and
acceleration.
 He understood how motion was possible and
that a body at rest was just a special case of a
body having constant velocity.
 Newton was able to carefully elucidate the
relationship between forces and acceleration.
Mechanics
-Newton’s laws
Newton’s first law
An object in motion with a constant velocity
will continue in motion unless acted upon
by some net external forces.
Mechanics
-Newton’s laws
Newton’s second law
The acceleration of a body is proportional to
the net external force and inversely
propostional to the mass of the body.
F  ma or
dp
F
dt
Mechanics
-Newton’s laws
Newton’s third law
The force exerted by body 1 on body 2 is
equal to and opposite to thehat body 2
exerts on body 1.
F21   F12
Electromagnetism
Electromagnetism developed over a
period of several hundred years.
 Important contributions were made by
Coulomb(1736-1806), Oersted(17771851), Young(1773-1829), Ampere(17751836), Faraday (1791-1867), Henry
(1797-1878), Maxwell (1831-1879), and
Hertz (1857-1894).

Electromagnetism

Maxwell showed that electricity and
magnetism were intimately connected and
were related by a change in the inertial frame
of reference.
 His work also led to the understanding of
electromagnetic radiation, of which light and
optics are special cases.
 Maxwell’s four equation, together with the
Lorentz force law, explain much of
electromagnetism.
James Clerk Maxwell






1831 – 1879
Developed the
electromagnetic theory
of light
Developed the kinetic
theory of gases
Explained the nature of
color vision
Explained the nature of
Saturn’s rings
Died of cancer
Electromagnetism

Gauss’s law for
electricity

Gauss’s law for
magnetism

Faraday’s law

Generalized Ampere’s
law
q
 E d A  
0
 B d A  0
d B
 E  d s   dt
d E
 B  d s  0 0 dt  0 I
F  qE  qv  B
Conduction Current, cont.



Ampère’s Law in this
form is valid only if the
conduction current is
continuous in space
In the example, the
conduction current
passes through only S1
This leads to a
contradiction in
Ampère’s Law which
needs to be resolved
Ampère’s Law,
General – Example

The electric flux through
S2 is EA





S2 is the gray circle
A is the area of the
capacitor plates
E is the electric field
between the plates
If q is the charge on the
plates, then Id = dq/dt
This is equal to the
conduction current
through S1
Plane em Waves


We will assume that the
vectors for the electric and
magnetic fields in an em
wave have a specific
space-time behavior that is
consistent with Maxwell’s
equations
Assume an em wave that
travels in the x direction
with the electric field in the
y direction and the
magnetic field in the z
direction
Thermodynamics

Thermodynamics deals with temperature T,
heat Q, work W, and the internal energy of
systems U.
 The understanding of the concepts used in
thermodynamics: pressure P, volume V,
temperature T, thermal equilibrium, heat,
entropy, and energy, was slow in coming.
 Important contributions to thermodynamics
were made by Benjamin Thompson (17531814), Carnot (1796-1832), Joule (18181889), Clausius (1822-1888), and Lord
Kelvin (1824-1907).
The Laws of Thermodynamics

First law of thermodynamics:
The change in the internal energy of a 
system
U is
equal to the heat Q added to the system minus
the work W done by the system.
U  Q  W
The Laws of Thermodynamics

Second law of thermodynamics:
It is not possible to convert heat
completely into work without some
other change taking place.
( 要將熱完全轉變成功而沒有任
何損耗是不可能的)
The Laws of Thermodynamics

Zeroth law of thermodynamics:
如果有兩個熱力學系統分別與第三個熱力學系
統進行熱接觸而達到熱平衡，則此兩個熱力學
系統必定達成熱平衡。
Zeroth Law of Thermodynamics,
Example

Object C (thermometer) is placed in contact with A until
it they achieve thermal equilibrium


Object C is then placed in contact with object B until
they achieve thermal equilibrium


The reading on C is recorded
The reading on C is recorded again
If the two readings are the same, A and B are also in
thermal equilibrium
Temperature
溫度可視為物質的一種性質可用來決
定它是否與其他物體已達成熱平衡
 兩物體若達成熱平衡必定具有相同的
溫度

The Laws of Thermodynamics

Third law of thermodynamics:
要達到絕對零度是不可能的
Energy at Absolute Zero
根據古典物理分子的動能在絕對零度時必定為
零
 因此分子必定都躺在箱子底部
 量子論指出在絕對零度時仍有殘餘的能量– 此
能量稱為零點能量

The kinetic Theory of Gases
分子動力論以粒子觀點來探討熱力學現象.
 Irist chemist Robert Boyle (1627-1681) :
(the Boyle’s law) 定溫時氣體的體積與壓
力的乘積保持定值

PV  constant
The kinetic Theory of Gases

The French physicist Charles (17461823) (the Charle’s law) 在定壓下氣體的
體積與溫度的比值保持定值:
V / T  constant
Idea Gas Equation

Combining the Boyle’s law and the
Charle’s law:
PV  nRT
Ideal Gas – Details

A collection of atoms or molecules that
Move randomly
 Exert no long-range forces on one another
 Are so small that they occupy a negligible
fraction of the volume of their container

Ideal Gas Law

The equation of state for an ideal gas
combines and summarizes the other gas laws
PV = n R T
 This is known as the ideal gas law
 R is a constant, called the Universal Gas
Constant


R = 8.314 J/ mol K = 0.08214 L atm/mol K
From this, you can determine that 1 mole of
any gas at atmospheric pressure and at 0o C is
22.4 L
Avogadro law
In 1811 the Italian physicist Avogadro
(1776-1856) proposed that equal
volume of gases at the same
temperature and pressure contained
equal numbers of molecules.
 This hypothesis was so far ahead of its
time that it was not accepted for many
years.

Bernoulli

Daniel Bernoulli (1700-1782) apparently
originated the kinetic theory of gases in
1738, but his result was generally
ignored.
Development

Many scientists, including Newton, Laplace, Davy,
Herapath, and Waterston, had contributed to the
development of kinetic theory by 1850.
 By 1895, the kinetic theory of gases was widely
accepted.
 The statistical interpretation of thermodynamics was
made in the latter half of the nineteenth century by the
great Scottish mathematical physicist Maxwell, the
Austrian physicist Ludwig Boltzmann (1844-1906),
and the american physicist Williard Gibbs (1839-1903).
Ludwid Boltzmann
1844 – 1906
 Contributions to





Kinetic theory of gases
Electromagnetism
Thermodynamics
Work in kinetic
theory led to the
branch of physics
called statistical
mechanics
Ideal Gas Notes
An ideal gas is often pictured as
consisting of single atoms
 However, the behavior of molecular
gases approximate that of ideal gases
quite well


Molecular rotations and vibrations have no
effect, on average, on the motions
considered
Pressure and Kinetic Energy

Assume a container
is a cube


Edges are length d
Look at the motion
of the molecule in
terms of its velocity
components
 Look at its
momentum and the
average force
Pressure and
Kinetic Energy, 2

Assume perfectly
elastic collisions
with the walls of the
container
 The relationship
between the
pressure and the
molecular kinetic
energy comes from
momentum and
Newton’s Laws
Pressure and
Kinetic Energy, 3

The relationship is
2  N   1 ___2 
P     mv 
3  V  2


This tells us that pressure is proportional
to the number of molecules per unit
volume (N/V) and to the average
translational kinetic energy of the
molecules
A Molecular Interpretation
of Temperature

We can take the pressure as it relates to
the kinetic energy and compare it to the
pressure from the equation of state for
an idea gas
2  N   1 ___2 
P     mv   NkBT
3  V  2


Therefore, the temperature is a direct
measure of the average translational
molecular kinetic energy
A Microscopic Description
of Temperature, cont

Simplifying the equation relating
temperature and kinetic energy gives
1 ___2 3
mv  kBT
2
2

This can be applied to each direction,
1 ___2 1
mv x  kBT
2
2
with similar expressions for vy and vz
A Microscopic Description
of Temperature, final

Each translational degree of freedom
contributes an equal amount to the
energy of the gas

In general, a degree of freedom refers to an
independent means by which a molecule
can possess energy
A generalization of this result is called
the theorem of equipartition of energy
(能量均分原理)

Theorem of
Equipartition of Energy
The theorem states that the energy of a
system in thermal equilibrium is equally
divided among all degrees of freedom
 Each degree of freedom contributes
½
kBT per molecule to the energy of the
system

Total Kinetic Energy

The total translational kinetic energy is just N
times the kinetic energy of each molecule
Etotal

 1 ___2  3
3
 N  mv   NkBT  nRT
2
2
 2
This tells us that the total translational kinetic
energy of a system of molecules is
proportional to the absolute temperature of the
system
Monatomic Gas

For a monatomic gas, translational kinetic
energy is the only type of energy the particles
of the gas can have
 Therefore, the total energy is the internal
energy:
3
Eint  n RT
2

For polyatomic molecules, additional forms of
energy storage are available, but the proportionality
between Eint and T remains
Distribution of
Molecular Speeds

The observed speed
distribution of gas
molecules in thermal
equilibrium is shown
 NV is called the
Maxwell-Boltzmann
distribution function
Distribution Function

The fundamental expression that describes
the distribution of speeds in N gas molecules
is
3
 mo  2 2  mv 2 2kBT
NV  4 N 
 v e
 2 kBT 

mo is the mass of a gas molecule, kB is
Boltzmann’s constant and T is the absolute
temperature
Average and
Most Probable Speeds

The average speed is somewhat lower
than the rms speed
8kBT
kBT
v 
 1.60
 mo
mo

The most probable speed, vmp is the speed
at which the distribution curve reaches a
peak
2k T
kT
v mp 
B
mo
 1.41
B
mo
Root Mean Square Speed

The root mean square (rms) speed is the
square root of the average of the
squares of the speeds


Square, average, take the square root
Solving for vrms we find
v rms

___
2
3 kBT
3 RT
 v 

m
M
M is the molar mass in kg/mole
Some Example vrms Values
At a given
temperature,
lighter
molecules
move faster,
on the
average, than
heavier
molecules
Speed Distribution

The peak shifts to the right as T increases



This shows that the average speed increases with increasing
temperature
The width of the curve increases with temperature
The asymmetric shape occurs because the lowest possible
Waves and Particles

Many aspects of physics can be treated as if
the bodies are simply particles, without internal
structure.
 Many natural phenomena can be explained
only in terms of waves, which are traveling
disturbances that carry energy.
 Waves and particles were the subject of
disagreement as early as the seventeenth
century, where there were two competing
theories of the nature of light.
Waves and Particles

Newton supported the idea that light consisted
of corpuscles (particles).
 He performed extensive experiments on light
for many years, and finally published his book
Opticks in 1704.
 Geometrical optics uses straight-line, particlelike trajectories called rays to explain familiar
phenomena like reflection and refraction.
 Geometrical optics was also able to explain
the apparent observation of sharp shadows.
Waves and Particles
Dutch physicist Christiaan Huygens
(1629-1695) presented his theory in
1678 befroe publishing in 1690.
 The wave theory could also explain
reflection and refraction, but it could not
explain the sharp shadows.

Diffraction Pattern, Penny

The shadow of a penny
displays bright and dark
rings of a diffraction
pattern
 The bright center spot is
called the Arago bright
spot

Named for its discoverer,
Dominque Arago
Diffraction Pattern,
Penny, cont

The Arago bright spot is explained by the wave
theory of light
 Waves that diffract on the edges of the penny
all travel the same distance to the center
 The center is a point of constructive
interference and therefore a bright spot
 Geometric optics does not predict the
presence of the bright spot

The penny should screen the center of the pattern
The Nature of Light

Before the beginning of the nineteenth century,
light was considered to be a stream of
particles
 The particles were emitted by the object being
viewed,


Newton was the chief architect of the particle
theory of light
He believed the particles left the object and
stimulated the sense of sight upon entering the
eyes
Nature of Light –
Alternative View
Christian Huygens argued the light
might be some sort of a wave motion
 Thomas Young (1801) provided the first
clear demonstration of the wave nature
of light

He showed that light rays interfere with
each other
 Such behavior could not be explained by
particles

More Confirmation
of Wave Nature
During the nineteenth century, other
developments led to the general
acceptance of the wave theory of light
 Maxwell asserted that light was a form of
high-frequency electromagnetic wave
 Hertz confirmed Maxwell’s predictions

Heinrich Rudolf Hertz
1857 – 1894
 Greatest discovery
was radio waves



1887
Showed the radio
waves obeyed wave
phenomena
 Died of blood
poisoning
Hertz’s Experiment

An induction coil is
connected to a
transmitter
 The transmitter
consists of two
spherical electrodes
separated by a
narrow gap
Particle Nature
Some experiments could not be
explained by the wave nature of light
 The photoelectric effect was a major
phenomenon not explained by waves

When light strikes a metal surface, electrons
are sometimes ejected from the surface
 The kinetic energy of the ejected electron is
independent of the frequency of the light

Dual Nature of Light
In view of these developments, light
must be regarded as having a dual
nature
 In some cases, light acts like a wave,
and in others, it acts like a particle

Properties of EM Waves
The solutions of Maxwell’s are wave-like,
with both E and B satisfying a wave
equation
 Electromagnetic waves travel at the
1
speed of light
c

oo

This comes from the solution of Maxwell’s
equations
Two Clouds on the Horizon
Blackbody
Radiation
Electromagnetic
Medium
Two Clouds on the Horizon
Blackbody Radiation

An object at any temperature is known to
emit thermal radiation
Characteristics depend on the temperature
and surface properties
 The thermal radiation consists of a
continuous distribution of wavelengths from
all portions of the em spectrum

Blackbody Radiation, cont

At room temperature, the wavelengths of the
thermal radiation are mainly in the infrared
region
 As the surface temperature increases, the
wavelength changes


It will glow red and eventually white
The basic problem was in understanding the
observed distribution in the radiation emitted
by a black body

Classical physics didn’t adequately describe the
observed distribution
Blackbody Radiation, final
A black body is an ideal system that
absorbs all radiation incident on it
 The electromagnetic radiation emitted by
a black body is called blackbody
radiation

Blackbody Approximation


A good approximation of
a black body is a small
hole leading to the
inside of a hollow object
The nature of the
radiation leaving the
cavity through the hole
depends only on the
temperature of the cavity
walls
Blackbody Experiment Results

The total power of the emitted radiation
increases with temperature




Stefan’s Law
P = s A e T4
For a blackbody, e = 1
The peak of the wavelength distribution shifts
to shorter wavelengths as the temperature
increases


Wien’s displacement law
lmax T = 2.898 x 10-3 m.K
Stefan’s Law – Details

P = s Ae T4
P is the power
 s is the Stefan-Boltzmann constant



s = 5.670 x 10-8 W / m2 . K4
Was studied in Chapter 17
Wien’s Displacement Law
 lmax
T = 2.898 x 10-3 m.K
lmax is the wavelength at which the curve
peaks
 T is the absolute temperature


The wavelength is inversely proportional
to the absolute temperature

As the temperature increases, the peak is
“displaced” to shorter wavelengths
Intensity of Blackbody Radiation,
Summary


The intensity increases
with increasing
temperature
The amount of radiation
emitted increases with
increasing temperature


The area under the
curve
The peak wavelength
decreases with
increasing temperature
Ultraviolet Catastrophe


At short wavelengths,
there was a major
disagreement between
classical theory and
experimental results for
black body radiation
This mismatch became
known as the ultraviolet
catastrophe

You would have infinite
energy as the
wavelength approaches
zero
Max Planck
1858 – 1947
 He introduced the
concept of “quantum
of action”
 In 1918 he was
awarded the Nobel
Prize for the
discovery of the
quantized nature of
energy

Planck’s Theory of
Blackbody Radiation

In 1900, Planck developed a structural model
for blackbody radiation that leads to an
equation in agreement with the experimental
results
 He assumed the cavity radiation came from
atomic oscillations in the cavity walls
 Planck made two assumptions about the
nature of the oscillators in the cavity walls
Planck’s Assumption, 1

The energy of an oscillator can have only
certain discrete values En

En = n h ƒ





n is a positive integer called the quantum number
h is Planck’s constant
ƒ is the frequency of oscillation
This says the energy is quantized
Each discrete energy value corresponds to a
different quantum state
Planck’s Assumption, 2

The oscillators emit or absorb energy only in
discrete units
 They do this when making a transition from
one quantum state to another


The entire energy difference between the initial and
final states in the transition is emitted or absorbed
as a single quantum of radiation
An oscillator emits or absorbs energy only when it
changes quantum states
Energy-Level Diagram




An energy-level
diagram shows the
quantized energy levels
and allowed transitions
Energy is on the vertical
axis
Horizontal lines
represent the allowed
energy levels
The double-headed
arrows indicate allowed
transitions
More discoveries

Discovery of X rays: Roentgen (1845-1923) in
1895
 Discovery of radioactivity: Henri Becquerel
(1852-1908) in 1896
 Discovery of electron: Michael Faraday in
1833; J.J. Thomson (1856-1940) in 1897
 Discovery of the Zeeman effect: Pieter
Zeeman (1865-1943) in 1896 found that
spectra lines were separated into two or three
lines when placed in magnetic field.
Problems bring the beginning of
modern physics
The problems existing in 1895 and the
important doscoveries of 1895-1897
bring us to the subject: modern physics.
 In 1900 Max Palnck completed his
radiation law, which solved the
blackbody problem bu required that
energy be quantized.
 In 1905 Einstein presented his three
important papers on Brownian motion,
the photoelectric effect, and special
relativity.
