Download Atomic Structure Lecture I

Chapter 23
The Early Atom & Quantum
Physics
When we consider the motion of objects on
the atomic level, we find that our classical
approach does not work very well.
For understanding motion on the
microscopic scale we must use Quantum
Mechanics.
ATOMIC STRUCTURE
Historical Development:
Greek Concepts of Matter
Aristotle - Matter is continuous, infinitely
divisible, and is composed of only 4 elements:
Earth, Air, Fire, and Water
 Won the philosophical/political battle.
 Dominated Western Thought for Centuries.
 Seemed very “logical”.
 Was totally WRONG!!
ATOMIC STRUCTURE
The “Atomists” (Democritus, Lucippus,
Epicurus, et. al.) - Matter consists ultimately
of “indivisible” particles called “atomos” that
canNOT be further subdivided or simplified.
If these “atoms” had space between them,
nothing was in that space - the “void”.
 Lost the philosophical/political battle.
 Lost to Western Thought until 1417.
 Incapable of being tested or verified.
 Believed the “four elements” consisted of
“transmutable” atoms.
 Was a far more accurate, though quite imperfect
“picture” of reality.
ATOMIC STRUCTURE
Modern Concepts of Matter
John Dalton (1803) - An atomist who formalized
the idea of the atom into a viable scientific theory
in order to explain a large amount of empirical
data that could not be explained otherwise.
 Matter is composed of small “indivisible” particles
called “atoms”.
 The atoms of each element are identical to each
other in mass but different from the atoms of other
elements.
 A compound contains atoms of two or more
elements bound together in fixed proportions
by mass.
ATOMIC STRUCTURE
Present Concepts - An atom is an electrically
neutral entity consisting of negatively charged
electrons (e-) situated outside of a dense, positively charged nucleus consisting of positively
charged protons (p+) and neutral neutrons (n0).
Particle
Electron
Proton
Neutron
Charge Mass
-1
9.109 x 10 -28 g
+1
1.673 x 10 -24 g
0
1.675 x 10 -24 g
ATOMIC STRUCTURE
Nucleus
Model of a
Helium-4
(4He) atom
e-
p+no
no p+
eElectron Cloud
How did we get this concept? - This portion of our
program is brought to you by:
Democritus, Dalton, Thompson, Planck, Einstein, Millikan,
Rutherford, Bohr, de Broglie, Heisenberg, Schrödinger,
Chadwick, and many others.
ATOMIC STRUCTURE
Democritus - First atomic ideas
Dalton - 1803 - First Atomic Theory
J. J. Thompson - 1890s - Measured the charge/mass
ratio of the electron (Cathode Rays)
Fluorescent
Material
_
Cathode
+
Anode
Electric Field
Source (Off)
With the electric field off, the cathode ray is not deflected.
ATOMIC STRUCTURE
-
Cathode
+
Anode
Fluorescent
Material
+
Electric Field
Source (On)
With the electric field on, the cathode ray is deflected
away from the negative plate. The stronger the electric
field, the greater the amount of deflection.
Cathode
+
Anode
Magnet
ATOMIC STRUCTURE
With the magnetic field present, the cathode ray is
deflected out of the magnetic field. The stronger the
magnetic field, the greater the amount of deflection.
e/m = E/H2r
e = the charge on the electron
m = the mass of the electron
E = the electric field strength
H = the magnetic field strength
r = the radius of curvature of the electron beam
Thompson, thus, measured the charge/mass ratio
of the electron - 1.759 x 108 C/g
ATOMIC STRUCTURE
Summary of Thompson’s Findings:
 Cathode rays had the same properties no matter
what metal was being used.
 Cathode rays appeared to be a constituent of all
matter and, thus, appeared to be a “sub-atomic”
particle.
 Cathode rays had a negative charge.
 Cathode rays have a charge-to-mass ratio
of 1.7588 x 108 C/g.
ATOMIC STRUCTURE
R. A. Millikan - Measured the charge of the electron.
In his famous “oil-drop” experiment, Millikan was able to
determine the charge on the electron independently of its
mass. Then using Thompson’s charge-to-mass ratio, he
was able to calculate the mass of the electron.
e = 1.602 10 x 10-19 coulomb
e/m = 1.7588 x 108 coulomb/gram
m = 9.1091 x 10-28 gram
Goldstein - Conducted “positive” ray experiments that
lead to the identification of the proton. The charge
was found to be identical to that of the electron and
the mass was found to be 1.6726 x 10-24 g.
ATOMIC STRUCTURE
Ernest Rutherford - Developed the “nuclear” model
of the atom.
The Plum Pudding Model of the atom:
+
+
+ +
+ +
Electrons
A smeared out “pudding”
of positive charge with
negative electron “plums”
imbedded in it.
The Metal Foil Experiments:
Radioactive
Material in
Pb box.
a-particles
Metal
Foil
Fluorescent
Screen
ATOMIC STRUCTURE
If the plum pudding model is correct, then all of
the massive a-particles should pass right through
without being deflected.
In fact, most of the a - particles DID pass right
through. However, a few of them were deflected at
high angles, disproving the “plum pudding” model.
Rutherford concluded from this that the atom consisted of a very dense nucleus containing all of the
positive charge and most of the mass surrounded
electrons that orbited around the nucleus much as
the planets orbit around the sun.
ATOMIC STRUCTURE
Problems with the Rutherford Model:
It was known from experiment and electromagnetic
theory that when charges are accelerated, they
continuously emit radiation, i.e., they lose energy
continuously. The “orbiting” electrons in the atom
were, obviously, not doing this.
 Atomic spectra and blackbody radiation
were known to be DIScontinuous.
 The atoms were NOT collapsing.
ATOMIC STRUCTURE
Atomic Spectra - Since the 19th century, it had
been known that when elements are heated until
they emit light (glow) they emit that light only at
discrete frequencies, giving a line spectrum.
-
+
Hydrogen
Gas
Line Spectrum
ATOMIC STRUCTURE
When white light is passed through a sample of
the vapor of an element, only discrete frequencies
are absorbed, giving a absorption ban spectrum.
These frequencies are identical to those of the
line spectrum of the same element.
For hydrogen, the spectroscopists of the 19th
Century found that the lines were related by the
Rydberg equation:
n/c = R[(1/m2) - (1/n2)]
n = frequency
c = speed of light
R = Rydberg Constant
m = 1, 2, 3, ….
n = (m+1), (m+2), (m+3), ….
Blackbody Radiation
One of the earliest indications that classical
physics was incomplete came from attempts to
describe blackbody radiation.
A blackbody is an ideal surface that absorbs all
incident radiation.
Blackbody radiation is the emission of
electromagnetic waves from the surface of an
object. The distribution of blackbody radiation
depends only the temperature of the object.
The Blackbody Distribution
The intensity spectrum
emitted from a blackbody has
a characteristic shape.
The maximum of the intensity
is found to occur at a
wavelength given by Wien’s
Displacement Law:
fpeak = (5.88  1010 s-1·K-1)T
T = temperature of blackbody
(K)
The Ultraviolet Catastrophe
Classical physics can describe the shape of the
blackbody spectrum only at long wavelengths.
At short wavelengths there is complete
disagreement.
This disagreement
between observations
and the classical theory
is known as the
ultraviolet catastrophe.
Planck’s Solution
In 1900, Max Planck was able to explain the
observed blackbody spectrum by assuming that
it originated from oscillators on the surface of
the object and that the energies associated with
the oscillators were discrete or quantized:
En = nhf
n = 0, 1, 2, 3…
n is an integer called the quantum number
h is Planck’s constant: 6.62  10-34 J·s
f is the frequency
Quantization of Light
Einstein proposed that light itself comes in
chunks of energy, called photons. Light is
a wave, but also a particle. The energy of
one photon is
E = hf
where f is the frequency of the light and h
is Planck’s constant.
Useful energy unit: 1 eV = 1.6  10-19 J
Quantum Mechanics
The essence of quantum mechanics is that
certain physical properties of a system (like
the energy) are not allowed to be just any
value, but instead must be only certain
discrete values.
Example
(a) Find the energy of 1 (red) 650 nm photon.
(b) Find the energy of 2 (red) 650 nm photons.
The PhotoElectric Effect
When light is incident on
a surface (usually a
metal), electrons can be
ejected. This is known
as the photoelectric
effect.
Around the turn of the century, observations of the
photoelectric effect were in disagreement with the
predictions of classical wave theory.
Observations of the Photoelectric Effect
• No electrons are emitted if the frequency of the
incident photons is below some cutoff value,
independent of intensity.
• The maximum kinetic energy of the emitted
electrons does not depend on the light
intensity.
• The maximum kinetic energy of the emitted
electrons does depend on the photon
frequency.
• Electrons are emitted almost instantaneously
from the surface.
The Photoelectric Effect Explained
(Einstein 1905, Nobel Prize 1921)
The photoelectric effect can be understood as follows:
• Electrons are emitted by absorbing a single photon.
• A certain amount of energy, called the work function,
W0, is required to remove the electron from the
material.
• The maximum observed kinetic energy is the
difference between the photon energy and the work
function.
Kmax = E – W0
E = photon energy
Walker Problem 25, pg. 1008
Zinc and cadmium have photoelectric work
functions given by WZn = 4.33 eV and WCd = 4.22
eV, respectively. (a) If both metals are illuminated
by UV radiation of the same wavelength, which one
gives off photoelectrons with the greater maximum
kinetic energy? Explain. (b) Calculate the
maximum kinetic energy of photoelectrons from
each surface if l = 275 nm.
The Mass and Momentum of a Photon
Photons have momentum, but no mass.
We cannot use the formula p = mv to find
the momentum of the photon. Instead:
hf
h
p=
=
c
l
The Wave Nature of Particles
We have seen that light is described sometimes
as a wave and sometimes as a particle.
In 1924, Louis deBroglie proposed that particles
also display this dual nature and can be
described by waves too!
The deBroglie wavelength of a particle is related
to its momentum:
l= h/p
(Use p = gmv if the velocity is large.)
Example
If a baseball, with a mass of 0.200 kg has
a speed of 45 m/s, what is its
wavelength?
Example
If an electron has a speed of 1.00  106
m/s, what is its wavelength?
Example
The maximum momentum of electrons at the
Jefferson Lab accelerator in Newport News is 6
GeV/c.
(a) What is the wavelength of those electrons?
(b) Why is the wavelength well suited to the study of
nuclear physics?