Physics of the Atom

1
Chapter 29

• Physics of the Atom

2
A Brief Overview of Modern Physics

• 20th Century revolution
• 1900 Max Planck
• Basic ideas leading to Quantum theory
• 1905 Einstein
• Special Theory of Relativity
• 21st Century
• Story is still incomplete

3
Basic Problems

• The speed of every particle in the universe
  always remains less than the speed of light
• Newtonian Mechanics is a limited theory
• It places no upper limit on speed
• It is contrary to modern experimental results
• Newtonian Mechanics becomes a specialized case of
  Einsteins Theory of Special Relativity
• When speeds are much less than the speed of light

4
Galilean Relativity

• Choose a frame of reference
• Necessary to describe a physical event
• According to Galilean Relativity, the laws of
  mechanics are the same in all inertial frames of
  reference
• An inertial frame of reference is one in which
  Newtons Laws are valid
• Objects subjected to no forces will move in
  straight lines

5
Galilean Relativity Example

• A passenger in an airplane throws a ball straight
  up
• It appears to move in a vertical path
• The law of gravity and equations of motion under
  uniform acceleration are obeyed

6
Galilean Relativity Example, cont

• There is a stationary observer on the ground
• Views the path of the ball thrown to be a
  parabola
• The ball has a velocity to the right equal to the
  velocity of the plane

7
Galilean Relativity Example, conclusion

• The two observers disagree on the shape of the
  balls path
• Both agree that the motion obeys the law of
  gravity and Newtons laws of motion
• Both agree on how long the ball was in the air
• Conclusion There is no preferred frame of
  reference for describing the laws of mechanics

8
Galilean Relativity Limitations

• Galilean Relativity does not apply to experiments
  in electricity, magnetism, optics, and other
  areas
• Results do not agree with experiments
• The observer should measure the speed of the
  pulse as vc
• Actually measures the speed as c

9
Newtonian Mechanics

• In the absence of forces, a body moves with
  uniform speed
• in a straight line.
• 2. In the presence of force, the body changes its
  state of motion
• in such a way that

Based on the premise of Absolute Space and
Absolute Time. Newton wrote Absolute space in
its own nature, without relation to any
external, remains always similar and immovable.
10
But because the parts of space cannot be seen,
or distinguished from one another by our senses,
therefore in their stead we use sensible measures
of them. For from the positions and distances
of things from any body considered as immovable,
we define all places and then with respect to
such places, we estimate all motions, considering
bodies are transferred from some of those places
into others. And so, instead of absolute places
and motions, we use relative ones and without
any inconvenience in common affairs. -
Isaac Newton -
However, Newton himself recognized that there is
an ambiguity in his argument.
Newtons law of mechanics holds true in any
inertial frames.
11
vx vx v vy vy vz vz
r (x,y,z) x x vt y y
z z
12
Luminiferous Ether

• 19th Century physicists compared electromagnetic
  waves to mechanical waves
• Mechanical waves need a medium to support the
  disturbance
• The luminiferous ether was proposed as the medium
  required (and present) for light waves to
  propagate
• Present everywhere, even in space
• Massless, but rigid medium
• Could have no effect on the motion of planets or
  other objects

13
Verifying theLuminiferous Ether

• Associated with an ether was an absolute frame
  where the laws of e m take on their simplest
  form
• Since the earth moves through the ether, there
  should be an ether wind blowing
• If v is the speed of the ether relative to the
  earth, the speed of light should have minimum or
  maximum values depending on its orientation to
  the wind

14
Michelson-Morley Experiment

• First performed in 1881 by Michelson
• Repeated under various conditions by Michelson
  and Morley
• Designed to detect small changes in the speed of
  light
• By determining the velocity of the earth relative
  to the ether

15
Michelson-Morley Equipment

• Used the Michelson Interferometer
• Arm 2 is aligned along the direction of the
  earths motion through space
• The interference pattern was observed while the
  interferometer was rotated through 90
• The effect should have been to show small, but
  measurable, shifts in the fringe pattern

16
Michelson-Morley Results

• Measurements failed to show any change in the
  fringe pattern
• No fringe shift of the magnitude required was
  ever observed
• Light is now understood to be an electromagnetic
  wave, which requires no medium for its
  propagation
• The idea of an ether was discarded
• The laws of electricity and magnetism are the
  same in all inertial frames

17
Einsteins Principle of Relativity

• Resolves the contradiction between Galilean
  relativity and the fact that the speed of light
  is the same for all observers
• Postulates
• The Principle of Relativity All the laws of
  physics are the same in all inertial frames
• The constancy of the speed of light the speed of
  light in a vacuum has the same value in all
  inertial reference frames, regardless of the
  velocity of the observer or the velocity of the
  source emitting the light

18
The Principle of Relativity

• This is a sweeping generalization of the
  principle of Galilean relativity, which refers
  only to the laws of mechanics
• The results of any kind of experiment performed
  in a laboratory at rest must be the same as when
  performed in a laboratory moving at a constant
  speed past the first one.
• No preferred inertial reference frame exists
• It is impossible to detect absolute motion

19
The Constancy of the Speed of Light

• Been confirmed experimentally in many ways
• A direct demonstration involves measuring the
  speed of photons emitted by particles traveling
  near the speed of light
• Confirms the speed of light to five significant
  figures
• Explains the null result of the Michelson-Morley
  experiment
• Relative motion is unimportant when measuring the
  speed of light
• We must alter our common-sense notions of space
  and time

20
Consequences of Special Relativity

• Restricting the discussion to concepts of length,
  time, and simultaneity
• In relativistic mechanics
• There is no such thing as absolute length
• There is no such thing as absolute time
• Events at different locations that are observed
  to occur simultaneously in one frame are not
  observed to be simultaneous in another frame
  moving uniformly past the first

21
In 19th century, physicists believed in
luminiferous ether and that Light travels with
the speed of light,c relative to this light
medium.
Now, lets consider the effect that we are making
this measurement on the surface of earth which
is moving through the ether with a speed v,
close to 18 miles/s
22
Moving with v
However, Michelson-Morleys experiment showed
with a high precision ttotal 2L/c
23
Accurate measurements of speed of light give the
value c 2.998 x 108 m/s no matter how the light
source or/and the measurer are moving!!
Serious conflict with then current understanding
based on Newtonian world.
In 1905, He provided a new view on
space-time,and proposed a new theory of
mechanics which is consistent with Newtonian
mechanics in the limit of low speed.
1921 Nobel Prize in Physics for his services to
Theoretical Physics, and especially for his
discovery of the law of the photoelectric
effect"
24
In his 1905 paper, Einstein proposes the same
law of electrodynamics and optics will be valid
for all frames of reference for which the
equation of mechanics hold good. We will raise
this conjecture (the purport of which will
hereafter be called the Principle of
Relativity) to the status of a postulate.
the experimental observation that the speed of
light is c regardless Of the reference frame
where the light source or the observer resides.

• Neither an object nor any form of energy can be
  accelerated to a speed
• as fast as or faster than c.
• The mass of an object increases when its speed
  increases.
• Mass is a form of energy in the sense that mass
  and energy can be
• interchanged.
• 4. An observer observes that the clock moving
  with a speed relative to
• the observer is clicking slower than his.
• 5. When a long object is moving fast in its
  length direction passing by an
• observer, the observer will measure the length
  of the object is shorter
• than that at rest relative to the observer.

25
Time Dilation
Einstein Clock
1 round trip time 2L/c
L
26
is longer than
27
Time Dilation, Summary

• The time interval ?t between two events measured
  by an observer moving with respect to a clock is
  longer than the time interval ?tp between the
  same two events measured by an observer at rest
  with respect to the clock
• A clock moving past an observer at speed v runs
  more slowly than an identical clock at rest with
  respect to the observer by a factor of