Transcript Quantum_Mechanics_1

Quantum Mechanics
Photoelectric Effect & The Ultraviolet
Catastrophe
Birth of Quantum Mechanics
Until about 1900, scientists only understood
electromagnetic radiation to be made up of
waves. Then in the early 1900s Max Plank
theorised that light was quantised, that it
came in discrete packages.
Max Planck stated that the light emitted by a
hot object (black body radiation) is given off
in discrete units or quanta. The higher the
frequency of the light the greater the energy
per quantum.
Quantum?
Quantum mechanics is the study of processes which
occur at the atomic scale.
The word "quantum" is derived
From Latin to mean BUNDLE.
Therefore, we are studying the motion of objects that
come in small bundles called quanta. These tiny
bundles that we are referring to are electrons
traveling around the nucleus.
Li
Na
Different atoms emit distinct light
K
Black Body Radiation
Hot objects emit radiation. The hotter they are the more they emit, at higher
energies. Thus hot objects show a characteristic pattern of light emission. This sort of
radiation is called black-body radiation.
Black Body Radiation
The term "black body" is used because none of the light is reflected from some other source and
the intrinsic color of the material is not important. A bar of gold and a bar of black graphite at
3000 degrees C would emit the same color light. The Sun is very close to a theoretical black body
in its light emission - all stars are. The Moon is not. The Moon absorbs sunlight and re-emits it in
different forms, for example, a lot of visible light is absorbed by the surface and re-emitted in
infrared. Incandescent lights, as befits their names, are pretty close to black-body emitters,
fluorescent, neon, and sodium-vapor lights are not.
As temperature increases, two things happen:
The object emits more radiation at all wavelengths.
The peak of maximum emission shifts toward higher-energy (blue) wavelengths. The very hottest
stars emit most of their radiation in the ultraviolet.
As an object heats up, the peak of emission creeps into the visible range and the familiar "red
hot" color appears. As the object gets still hotter, the peak shifts into the yellow part of the
spectrum and the object glows orange, then yellow. But then the object becomes a paler yellow
and finally white, not green. Why? When the emission peak is in the green (as it actually is for the
Sun!), the object is still emitting copious red and yellow light, and these wavelengths combine to
give a fairly pure white. But the very hottest stars have peaks in the violet and beyond, and their
blue and violet emission is so much greater than their red and yellow that the stars appear bluewhite.
The Ultraviolet Catastrophe
This was a CLASSICAL
prediction, first made in the late
19th century, that an IDEAL
BLACK BODY at thermal
equilibrium will emit radiation
with INFINITE POWER.
Max Planck resolved this issue by
postulating that electromagnetic
energy did not follow the classical
description, but could only
oscillate or be emitted in
DISCRETE PACKETS OF
ENERGY proportional to the
frequency. He called these packets
‘QUANTA’.
Note:
h  6.626 x10 34 J .s
E  h
1900 - Rayleigh
Plank’s Constant
Planck’s constant, (symbol h), fundamental physical constant characteristic of the
mathematical formulations of quantum mechanics, which describes the behavior
of particles and waves on the atomic scale, including the particle aspect of light.
The German physicist Max Planck introduced this constant in 1900 in his accurate
formulation of the distribution of the radiation emitted by a blackbody, or a
perfect absorber of light. The significance of the context is that radiation, such as
light is emitted, transmitted, and absorbed in discrete energy packets, or quanta,
determined by the frequency of the radiation and the value of Planck’s constant.
The energy E of each quantum, or each photon, equals Planck’s constant h times
the radiation frequency symbolized by the Greek letter nu, ν, or simply E = hν.
The dimension of Planck’s constant is the product of energy multiplied by time, a
quantity called action. Planck’s constant is often defined, therefore, as the
elementary quantum of action. Its value in metre-kilogram-second units is
6.62606957 × 10−34 joule∙second, with a standard uncertainty of
0.00000029 × 10−34 joule∙second.
Light is a Particle
Albert Einstein, one of the few
scientists to take Planck's ideas
seriously, proposes a quantum of
light (the photon) which behaves
like a particle in 1905. Therefore,
light consisted of photons.
A photon is a “particle” or
“packet” of energy.
A photon has an energy of E = hf
where h is called Planck’s constant
and f is frequency.
High frequency (low wavelength)
photons have high energy; low
frequency (high wavelength)
photons have low energy.
“Newton, forgive me..”, Albert
Einstein
At the atomic scale Newtonian Mechanics
cannot seem to describe the motion of
particles. An electron trajectory between
two points for example IS NOT a perfect
parabolic trajectory as Newton's Laws
predicts. Where Newton's Laws end
Quantum Mechanics takes over.....IN A
BIG WAY!
One of the most popular concepts
concerning Quantum Mechanics is called ,
“The Photoelectric Effect”. In 1905, Albert
Einstein published this theory for which he
won the Nobel Prize in 1921.
Properties of Photons
POSTULATE
Electromagnetic radiation
can be viewed as a stream
of particle-like units called
photons
E  h
The photoelectric
effect.
Work Function
Work function, f, is defined as the least energy that must
be supplied to remove a free electron from the surface
of the metal, against the attractive forces of
surrounding positive ions.
Shown here is a PHOTOCELL. When
incident light of appropriate frequency
strikes the metal (cathode), the light
supplies energy to the electron. The
energy need to remove the electron from
the surface is the WORK!
Not ALL of the energy goes into work! As
you can see the electron then MOVES
across the GAP to the anode with a
certain speed and kinetic energy.
Maximum K.E.
The MAXIMUM KINETIC ENERGY is the energy difference between the
MINIMUM AMOUNT of energy needed (ie. the work function) and the
LIGHT ENERGY of the incident photon.
Light Energy, E
The energy NOT used to
do work goes into
KINETIC ENERGY as the
electron LEAVES the
surface.
WORK done to remove
the electron
THE BOTTOM LINE: Energy Conservation must still hold true!
Photoelectric effect
Photoelectric Effect
The emission of electrons from
a surface (usually metallic)
upon exposure to, and
absorption of, electromagnetic
radiation.
The photoelectric effect was
explained mathematically by
Einstein who extended the
work on QUANTA as deloped
by Planck.
KE = hf - j
Quantum Effects and Photons
Photoelectric Effect
– The photoelectric effect is the ejection of electrons
from the surface of a metal when light shines on it.
– Electrons are ejected only if the light exceeds a certain
“threshold” frequency.
– Violet light, for example, will cause potassium to eject
electrons, but no amount of red light (which has a
lower frequency) has any effect.
Photo Electric Effect
Photoelectric effect
– For a given metal, a
certain amount of
energy is needed to eject
the electron
– This is called the work
function
– Since E=h, the photons
must have a frequency
higher than the work
function in order to eject
electrons
Planck’s Constant
Make sure you USE the correct constant!
h
6.63x10-34 Js
4.14x10-15 eVs
hc
1.99x10-25 Jm
1.24x103 eVnm
Planck’s Constant is the SLOPE of an
Energy vs. Frequency graph!
E
E  f  E  hf   h
f
c
hc
 f E


Threshold Frequency
The frequency of radiation must be above a certain value before the
energy is enough. This minimum frequency required by the source of
electromagnetic radiation to just liberate electrons from the metal is
known as threshold frequency, f0.
The threshold frequency is
the X-intercept of the
Energy vs. Frequency
graph!
Equations
E  hf
K  W  hf
K  hf  W  K  hf  f
y  mx  b
KINETIC ENERGY can be plotted on the y axis and FREQUENCY on the x-axis. The
WORK FUNCTION is the y – intercept as the THRESHOLD FREQUNECY is the x
intercept. PLANCK‘S CONSTANT is the slope of the graph.