2. What is Modern Physics?
1- Introduction
• Modern physics only came in the 1900’s.
• Physicists discovered that Newtonian
mechanics did not apply when objects were
very small or moved very fast!
• If things are confined to very small dimensions
(nanometer-scale), then QUANTUM
mechanics is necessary.
• If things move very fast (close to the speed of
light), then RELATIVISTIC mechanics is
necessary.
3. 2- The wave-Particle duality
Young's double slit experiment
This was one of the defining
characteristics of waves
Interference of light waves
4. The electron exhibits
a dual nature, with
both particle-like
behavior and wave-
like behavior.
Very short exposure
14 photon impacts
Longer exposure
~150 photon impacts
Much longer exposure
a few thousand
photon impacts
5. • Waves can exhibit particle-like
characteristics, and particles can
exhibit wave-like characteristics.
6. 3- Blackbody radiation and Planck's constant
The electromagnetic radiation emitted by a
perfect blackbody at two different temperatures.
We see the glow of hot
objects because they
emit electromagnetic
waves in the visible
region of the spectrum.
A perfect blackbody at
a constant temperature
absorbs and reemits all
the electromagnetic
radiation falls on it.
7. • In 1900 Planck calculated the blackbody
radiation curves, using a model that
represents a blackbody as a large number of
atomic oscillators. Planck assumed that the
energy E of an atomic oscillator could have
only the discrete values of
• E = 0, h f, 2 h f, 3 h f, and so on.
• E = n h f n = 0, 1, 2, 3, . . . ,
n is a positive integer
f is the frequency of vibration (in hertz)
h is a constant called Planck's constant.
8. • Experiment has shown that
Planck's constant has a value of:
h = 6.6260755 x 10-34 j.s
• The energy of a system can have only certain
definite values, and nothing in between, the
energy is said to be quantized.
Max Planck
(1858-1947)
9. 4- The photoelectric effect
Light consists of
photons
Electrons emitted
from a metal surface
when light shines on
it.
Light shines on a metal surface, and
electrons are ejected from the surface.
These photoelectrons are drawn to the
positive collector, thus producing a
current
10. • Einstein proposed that light of frequency f
could be regarded as a collection of discrete
packets of energy (photons), each packet
containing an amount of energy E given by :
E = h f
where h is the Planck's constant.
11. • According to Einstein, when light shines on a
metal, a photon can give up its energy to an
electron in the metal.
• If the photon has enough energy to do work of
removing the electron from the metal, the
electron can be ejected.
• The work required depends on how strongly
the electron is held.
• For the strongly held electrons, the necessary
work has a minimum value W0 and is called
the work function of the metal.
12. • If a photon has energy in excess of the work
needed to remove an electron, the excess
energy appears as kinetic energy of the
ejected electron.
• Thus the least strongly held electrons are
ejected with the maximum kinetic energy
KEmax .
13. • Einstein applied the conservation of energy
principle and proposed the following relation
to describe the photoelectric effect:
h f = KEmax + Wo
Photon Maximum Minimum
energy kinetic energy work needed
of ejected e to eject e
14. Photons of light can eject
electrons from a metal when
the light frequency is above fo
Applications:
The moving
photoelectrons
constitute a current that
change as the intensity
of the light changes.
For example,
Safety feature of
automatic door openers
15. 5- The Compton effect
• Compton used the photon
model to explain his
research on the scattering
of X rays by the electrons
in graphite.
16. In an experiment performed by
Compton, an X-ray photon collides
with a stationary electron.
X-ray photon strikes an
electron in a piece of
graphite.
Like two billiard balls
colliding on a pool
table, the X-ray photon
in one direction, and
the recoil electron in
another direction after
the collision.
17. • The scattered photon has a frequency f ' that is
smaller than the frequency f of the incident
photon, indicating that the photon loses
energy during the collision.
• the difference between the two frequencies
depends on the angle θ at which the scattered
photon leaves the collision.
• The phenomenon in which an X-ray photon is
scattered from an electron, the scattered
photon having a smaller frequency than the
incident photon, is called the Compton effect.
18. • The electron is assumed to be initially at rest
and essentially free.
• In the collision between a photon and an
electron, the total kinetic energy and the total
linear momentum are the same before and
after the collisions, So according to the
principle of conservation of energy:
• h f = h f ' + KE
energy of energy of kinetic energy
incident scattered of recoil
photon photon electron
19. • Since λ ' = c / f ' , the wavelength of the
scattered X-rays is larger than that of the
incident X-rays. For an initially stationary
electron, conservation of linear momentum
requires that:
Dividing those two
equations, we find that
20. • Since a photon travels at the speed of light, v
= c and . Therefore, the momentum of a
photon . But the energy of a photon is
• , while the wavelength is , the magnitude of
the momentum is
21. • Compton showed that the difference between
the wavelength λ' of the scattered photon and
the wavelength λ of the incident photon is
related to the scattering angle θ by
• The quantity h/mc is referred to as the
Compton wavelength of the electron, and has
the value h/mc = 2.43 x 10-12 m .
22. • Since cos θ varies between +1 and -1,
the shift (λ' – λ) in the wavelength can vary
between zero and (2h / mc), depending on the
value of θ, a fact observed by Compton.
23. 6- The de Broglie Wavelength
• In 1923 Louis de Broglie made
the suggestion that since light
waves could exhibit particle-
like behavior, particles of
matter should exhibit wave-
like behavior.
• De Broglie proposed that all
moving matter has a
wavelength associated with it,
just as wave does.
Louis V. de Broglie
(1892-1987)
24. • De Broglie made the explicit proposal that the
wavelength λ of a particle is given by the same
relation that applies to a photon :
• h is the Planck's constant and p is the
magnitude of the relativistic momentum of
the particle.
• The effects of this wavelength are observable
only for particles whose masses are very
small, on the order of the mass of an electron
or a neutron.
25. 28e- 104 e-
Young's double slit experiment for electrons. The characteristic fringe
pattern becomes recognizable only after a sufficient number of electrons
have struck the screen.
26. • Bright fringes occur where there is a high
probability of electrons striking the screen,
and dark fringes occur where there is a low
probability.
• Particle waves are waves of probability, waves
whose magnitude at a point in space gives an
indication of the probability that the particle
will be found at that point.
27. • This probability is proportional to the square
of the magnitude Ψ (psi) of the wave. Ψ is
referred to as the wave function of the
particle.
• In 1925 Erwin Schrodinger and Werner
Heisenberg independently developed
theoretical frameworks for determining the
wave function; they established a new branch
of physics called Quantum Mechanics
28. 7- The Heisenberg Uncertainty principle
• Since there are number of bright
fringes, there is more than one
place where each electron has
some probability of hitting. Any
given electron can strike the
screen in only one place after
passing through the double slit.
• As a result, it is not possible to
specify in advance exactly where
on the screen an individual
electron will hit.
29. • Because the wave nature of particles is
important, we lose the ability to predict with
100 % certainly the path that a single particle
will follow. Instead only the average behavior
of large numbers of particles is predictable,
and the behavior of any individual particle is
uncertain.
30. A pattern due to the wave nature
of the electrons and is
analogous to that produced by
light waves.
Fig. shows the slit
and locates the first
dark fringe on either
side of the central
bright fringe. The
central fringe is
bright because
electrons strike the
screen over the
entire region
between the dark
fringes.
31. • the extent to which the electrons are
diffracted is given by the angle θ in the
drawing. To reach locations within the central
fringe, some electrons must have acquired
momentum in the y direction, despite the fact
that they enter the slit traveling along the x
direction and have no momentum in the y
direction to start with.
32. • The y component of the momentum may be
as large as Δ py . The notation Δ py indicates
the difference between the maximum value of
the y component of the momentum after the
electron passes through the slit and its value
of zero before the electron passes the slit. Δ py
indicates the uncertainty in the y component
of the momentum, in that a diffracted
electron may have the value from zero to Δ py
.
33. • We relate Δ py to the width W of the slit.
• We take the equation of the de Broglie wave
length λ, sin θ = λ / W
• If θ is small , sin θ ≈ tan θ ,
• from Fig. tan θ = Δ py / px , where px is the x
component of the momentum of the electron.
Therefore, Δ py / px ≈ h / λ according to de
Broglie's equation, so that
34. • a smaller slit width “a” leads to a larger
uncertainty in the y component of the
electron's momentum. Since the electron can
pass through anywhere over the width W, the
uncertainty in the y position of the electron is
Δy = a .
• Substituting for a shows that
Δ py ≈ h / Δ y , or
(Δpy) (Δy) ≈ h .
35. • The Heisenberg uncertainty principle:
• For momentum and position:
• Δy = uncertainty in a particle's position along
the y direction,
• Δpy = uncertainty in the y component of the
linear momentum of the particle
36. For energy and time:
• ΔE = uncertainty in the energy of a particle
when the particle is in a certain state,
• Δt = time interval during which the particle is
in the state
37. • The Heisenberg uncertainty principle places
limits on the accuracy with which the
momentum and position of a particle can be
specified simultaneously, it states that:
• it is impossible to specify precisely both the
momentum and position of a particle in the
same time.
• The same apply for uncertainty that deals with
energy and time
38. 8- The Shrödinger equation
• The wave function for de
Broglie waves must satisfy
an equation developed by
Shrödinger.
• One of the methods of
quantum mechanics is to
determine a solution to this
equation, which in turn
yields the allowed wave
functions and energy levels
of the system.
Erwin Schrödinger
(1887-1961
39. • the general form of the wave equation for
waves traveling along the x axis:
• Where v is the wave speed and where the
wave function ψ depends on x and t.
• We consider systems in which the total energy
E remains constant.
40. • Since E = h f, the frequency of de Broglie wave
also remains constant. In this case, we can
express the wave function ψ (x,t) as the
product of a term that depends only on x and
a term that depends only on t:
ψ (x, t) = ψ (x) cos(ω t)
Where v is the wave speed and where the
wave function ψ depends on x and t.
41. We consider systems in which the total energy
E remains constant. Since E = h f, the
frequency of de Broglie wave also remains
constant. In this case, we can express the
wave function ψ (x,t) as the product of a term
that depends only on x and a term that
depends only on t:
ψ (x, t) = ψ (x) cos(ω t)
42. Recall that ω = 2 π f = 2 π v / λ and, for de Broglie
waves, p = h / λ . Therefore,
43. • Furthermore, we can express the total energy
E as the sum of the kinetic energy and the
potential energy:
E = K + U = ( p2 /2 m ) + U
So that
P2 = 2 m ( E – U ) And
44. • This is the famous Schrödinger equation as it
applies to a particle confined to moving along
the x axis. Because this equation is
independent of time, it is commonly referred
to as the time-independent Schrödinger
equation.
