Physics 123C Waves

1
Physics 123C Waves
Lecture 21Nuclei and Spectra May 23, 2005

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

2
Lecture 21 Announcements

• Lecture Homework 6 has been posted on the
  Tycho system. It is due at 900 PM Wednesday,
  May 25.
• We will have Exam 3 on Friday. The exam will
  have a Lecture multiple-choice section (55
  points), a Lecture long-answer section (25
  points) and a Tutorial section (20 points). Look
  up you seat before the exam and bring a Scantron
  sheet, a calculator with good batteries, and one
  page of notes. Due to the tight lecture
  schedule, we will not have a pre-exam review on
  Wednesday.

3
Lecture Schedule (Weeks 7-10)
We are here
4
Thomsons Plum-Pudding Model
In 1900 it was clear that atoms have sizes
10-10 m and are divisible into sub-atomic parts
that are charged. It was also clear that
electrons are common to all atoms, are much
smaller than atoms, and much have less mass than
the lightest atom. But how do the electrons
fit into a atom? What holds the positive
charge of the atom? Where are the charge and
mass of atoms located?
J. J. Thomson proposed the first atomic
model. He reasoned that since the electrons are
small, the positive charge must occupy most of
the space. He proposed that atoms consist of a
cloud of positive charge roughly 10-10 m in
diameter in which electrons are embedded like
plums in a pudding. Thus, this is often called
Thomsons plum-pudding model of the atom
5
The Discovery of Radioactivity
In 1896, Antoine Henri Becquerel announced
the discovery of a new form of rays that were
emitted from crystals of uranium and could expose
photographic film and ionize air. He showed that
unlike X-rays, these rays could be deflected by
electric or magnetic fields. In 1898 the
Curies discovered radium and polonium by the
chemical fractionation of pitchblende, which was
known to be a stronger source of radiation than
uranium.
6
Rutherford and a Radioactivity
Ernest Rutherford, a student of J. J.
Thomson, began to study radioactivity. He
quickly discovered that uranium emitted at least
two distinctly different kinds of rays. The kind
that were easily absorbed he called alpha (a)
rays, while the more penetrating ones he called
beta (b) rays.

Thomson found that b rays were negative and
had the same q/m as cathode rays. Rutherford,
using the same techniques, found that a rays were
positive and had q/m ½e/mH, where mH is the
atomic mass of hydrogen.
This result could be interpreted as
indicating that a rays were either singly ionized
hydrogen molecules (H2) or doubly ionized helium
atoms (He). Rutherford sealed a radium sample
into a glass discharge tube, allowed the radium
to decay for several days, and then observed the
spectral lines in the discharge. They were the
lines for helium, not hydrogen. Therefore, a
rays were doubly ionized helium atoms (i.e., bare
helium nuclei) emitted at velocities of about
0.1c. Apparently some atoms are unstable and
spontaneously split into two or more charged
particles, including He.
7
The First Nuclear Physics Experiment
In 1909 Rutherford, with his students Hans
Geiger and Ernest Marsden, set up the experiment
shown in the figure to shoot a particles at very
thin metal foils. They found that the beam of
alpha particles that penetrated the foil became
somewhat spread out. Rutherford suggested that
Geiger and Marsden look for particles deflected
at large angles.

They found that not only were many a
particles scattered at large angles, but some
were scattered at almost 1800, i.e., straight
back at the source. Such scattering would
require an extremely large Coulomb force.
This resulted effectively falsified the Thomson
plum-pudding model, because in such a system the
positive and negative charges nearly cancel and
there are no electrical forces strong enough to
make 1800 scattering.
8
Rutherford Scattering
The implication of the Geiger-Marsden
observation of 1800 scattering of a particles is
that the electrical force is extremely strong,
requiring that all the positive charge and mass
of the gold atoms must be concentrated in a
region much smaller than the atom. Therefore,
this constituted the discovery of the atomic
nucleus.
9
ExampleA Nuclear Physics Experiment
An a particle is shot with a speed of 2.0 x
107 m/s directly toward the nucleus of a gold
atom. What is the distance of closest
approach to the gold nucleus.
10
Clicker Question 1
Which way will the a particle be deflected
by the magnetic field?

• Up
• Down
• Into the page
• Out of the page
• Backward at 1800

11
The Electron Volt
A joule is an appropriate unit for mechanics
and thermodynamics, but it is much too big for
use in atomic and nuclear physics. The
electron-volt (or eV) is the energy gained an
electron when accelerated through a potential of
1 V.
-
Other units 1 keV103 eV 1 MeV106 eV 1
GeV109 eV 1 TeV1012 eV
12
ExampleThe Speed of an Alpha Particle
Alpha particles usually are characterized by
their kinetic energy in MeV. What is the
velocity of an 8.30 MeV alpha particle?
13
ExampleEnergy of an Electron
In a simple model of hydrogen, the electron
orbits the proton at 2.19x106 m/s in a circle
with a radius of 5.29x10-11 m. What is the
atoms energy in eV?
14
Using the Nuclear Model
Rutherfords nuclear model of the atom makes
it easy to understand and visualize the process
of ionization. The electrons are in orbits
around the positively-charged nucleus. An
X-ray or a rapidly moving electron can knock one
or more orbital electrons out, leaving behind a
positively charged ion. If one electron is
removed, the ion will have a net charge of q
e. If two electrons are removed, the ion will
have a net charge of q 2e. The model also
explains how ions can carry currents in solutions
and how amber rods can become charged by rubbing.
15
Example The IonizationEnergy of Hydrogen
In a simple model of hydrogen, the electron
orbits the proton at 2.19x106 m/s in a circle
with a radius of 5.29x10-11 m. What is the
minimum energy required to ionize hydrogen?
16
Clicker Question 2
Carbon is the 6th element in the periodic
table. How many electrons orbit the nucleus
in a C ion?

• 0
• 1
• 2
• 4
• 6

17
Into the Nucleus
In 1869, Mendeleev arranged the chemical
elements in order of ascending mass and noted
certain regularities in their chemical
properties, to produce the periodic table of the
elements. This led to assigning an atomic number
Z to each element, denoting its place in the
periodic table. In the late 1800s it was
found that hydrogen could be singly ionized to
H, but not doubly ionized. Helium could be
doubly ionized to He, but not triply ionized.
After the work of Thomson and Millikan, it became
fairly clear that hydrogen contained only 1
electron, helium had 2, lithium had 3, so that Z
electron . The hydrogen nucleus was
recognized to be a proton, a heavy particle with
a charge of e. But there was a problem if
hydrogen is taken as mass 1, helium had mass 4
and lithium had mass 7. J. J. Thomson and
his student Francis Aston developed the mass
spectrometer. They discovered that one element
might have several masses (now called isotopes).
18
Chadwick and The Neutron
The mystery of isotope masses was solved by
James Chadwick. In 1928, Boethe and Becker had
found that when beryllium was exposed to a
particles from polonium, it gave off a
penetrating electrically-neutral radiation. The
Irene and Frederic Joliot-Curie found that the
neutral radiation ejected protons from paraffin.
In 1932 Chadwick repeated the measurements, also
exposing helium, nitrogen, and other elements to
the neutral radiation. He built a convincing
case that the neutral particle was a neutron, an
electrically neutral particle with essentially
the same mass as the proton.
Neutrons reside in the nucleus, giving it
mass but not charge. The isotopes of a given
element all have Z protons but differ in the
neutron number N.
19
Atomic Emission of Light
The positive column glow of Faradays gas
discharge tube, the color of which depended on
the type of gas used, stimulated interest as a
possible method of chemical identification.
Fortunately, developments in the diffraction and
interference of light at about the same time made
possible the grating spectrograph, which could
analyze the light into wavelengths with high
precision. The spectrograph measurements
showed that(1) the gas discharge emits light at
discrete wavelengths (called lines), and(2) the
line spectrum of each element in the periodic
table is unique.
20
Absorption Spectra
Materials not only emit light, but they can
also absorb light. If white light is passed
through a gas as shown, the absorption in the gas
removes certain wavelengths, so that the
spectrograph shows an absorption spectrum, a
spectrum of white light with certain wavelengths
missing. Comparison of the emission and
absorption spectra of the same element show a
provocative difference. Some of the lines are
present in both, but the emission spectrum
contains some lines missing in the absorption
spectrum. The classical physics of the 1800s
was unable to account either for spectral lines
or for the emission vs. absorption differences.
21
Clicker Question 3
Two spectra of the same element are shown.
Which is the absorption spectrum?
22
The Mystery of Balmers Formula
As mentioned in Lecture 19, the emission
spectrum lines of hydrogen appear to be very
simple and regular. Johann Balmer, by trial and
error, found a simple formula that predicted the
wavelengths of these lines. Later
investigations in the infrared and ultraviolet
showed that Balmers formula could be extended to
predict every line in the hydrogen spectrum,
using the generalized form
However, all attempts to derive Balmers
formula from Newtonian mechanics failed. Nature
was clearly sending a message, but no one could
decode it. It required 30 years more before
Neils Bohr finally solved the mystery of Balmers
formula.
23
Classical Physics at the Limit
Rutherfords nuclear atom model matched
experimental evidence about the structure of
atoms, but it had a fundamental shortcoming it
was inconsistent with Newtons mechanics and
Maxwells electromagnetic theory. In
particular, on electron orbiting a nucleus would
represent an oscillating charge that should
radiate a broad spectrum of electromagnetic
radiation, not lines. Further, the loss of
energy by such radiation should cause the
orbiting electron to spiral into the nucleus.
As the 20th century dawned, physicists could
not explain the structure of atoms, the stability
of matter, discrete spectral lines, emission and
absorption spectra differences, or the origins of
X-rays and radioactivity.
24
Five Things You Should Have Learned from This
Lecture

• J. J. Thomson proposed the plum-pudding model of
  atomic structure to account for the presence and
  detachability of electrons in atoms.
• Henri Becquerel discovered that uranium is
  radioactive and will expose photographic plates
  and discharge an electroscope.
• Ernest Rutherford and his students discovered
  that alpha particles can be scattered at 1800 by
  gold, falsifying the plum-pudding model and
  leading Rutherford to the nuclear model of the
  atom.
• Mass spectroscope measurements revealed that many
  elements have isotopes of differing masses.
  Chadwicks discovery of the neutron provided an
  explanation isotopes have the same Z but
  differing N.
• For a given element the absorption spectrum shows
  lines matching those of from emission, but the
  emission spectrum has extra lines.

25
Chapter 37 - Summary (1)
26
Chapter 37 - Summary (2)
27
End of Lecture 21

• Lecture Homework 6 is due at 900 PM on
  Wednesday, May 25.
• We will have Exam 3 on Friday. The exam will
  have a Lecture multiple-choice section (55
  points), a Lecture long-answer section (25
  points) and a Tutorial section (20 points). Look
  up you seat before the exam can bring a Scantron
  sheet, a calculator with good batteries, and one
  page of notes. We will not have a pre-exam
  review.
• Read Knight, Chapter 38.1-4 for Wednesday, May
  25.