Download Particle Nature of Matter

Particle Nature of Matter
Chapter 4
September 09
Modern Physics
Modern physics
When my grandfather was born, atoms were just an idea.
That year, 1897, was marked by the discovery of the
electron by J.J. Thomson.
The nuclear model was established by Rutherford,
Geiger and Marsden in 1913.
And in that year, Bohr produced the first quantum model
of the atom.
September 09
Modern Physics
Atomic physics
Chemistry suggests the idea of elemental substances
Complications:
Masses of most common isotopes are not quite
proportional to atomic number.
Isotopes: Fixed atomic number can have different
mass
Alloys, mixtures
September 09
Modern Physics
Electrical nature of atoms
The polar nature
of water
molecules
dissociates salts.
Ion curent
reveals a
relationship
between charge
and mass in
chemical
reactions.
September 09
Modern Physics
Electrical nature of atoms
In electrolysis of
NaCl, 96,500 C
of charge passes
while 23 gm of
Na is deposited
and 35.5 gm of Cl
gas formed.
Why? Formation
of ions with
quantized charge.
September 09
Modern Physics
Cathode rays
Cathode rays were discovered as emissions from
negatively charged metal elements.
September 09
Modern Physics
Thomson’s experiments
Electrons from the cathode are accelerated
through anode slits and deflected with electric
and magnetic fields.
September 09
Modern Physics
Charge to mass ratio
For an electric or a magnetic force, the
acceleration and deflection are proportional to
q/m - neither q nor m is determined
independently.
An independent measurement of the electron
charge would permit derivation of the electron
mass. => Millikan’s oil drop experiment.
September 09
Modern Physics
Speed of electron in CRTs
For accelerating potential V~ kV, the axial velocity
is given by (nonrelativistic) energy conservation
1/2 mv^2=qV=>v=[2qV/m]^1/2
Work it out - the speed is fast but 1 keV<<511
keV so v<<c.
Thomson did not have the means to measure the
travel time.
September 09
Modern Physics
Millikan’s experiment
Observe singly
charged
microscopic drops
levitated by an
electric field.
Force balance
mg =qE
gives charge as
q=mg/E
September 09
Modern Physics
Millikan’s experiment
What radius drop with net charge e can be suspended
between two plates of separation h= 1 cm and voltage V?
September 09
Modern Physics
Millikan’s experiment
What radius drop with net charge e can be suspended
between two plates of separation h= 1 cm and voltage V?
September 09
Modern Physics
Conclusions
The charge to mass ratio q/m and the charge
e give the electron mass
Gulp: Electrons determine electrical/chemical
properties of elements BUT the mass of an atom is
not electronic!
September 09
Modern Physics
Quark searches
In the 1970s, particle physics was focused on
“fractionally charged” quarks - d-1/3 an u+2/3.
The proton composition is p=uud.
The neutron compositions is n = udd.
The Millikan experiment was repeated with laser jet
printing technology. No fractionally charged drops
were found. Quarks are confined by incredibly
strong color forces into “color” neutral composites.
Free quarks were not observed.
September 09
Modern Physics
Rutherford scattering
Radioactivity provides high energy particles
capable of probing the atomic nucleus.
An “alpha” particle emitted in nuclear decay has
kinetic energy of several MeV typical of nuclear
energy scales.
September 09
Modern Physics
Rutherford scattering
Rutherford, Geiger,
Marsden studied
alpha scattering
from thin foils of
metal.
September 09
Modern Physics
Nuclear scattering model
Most likely is a
collision with large
impact
parameter/distance
from nucleus, and
with small scattering
angle. Large angle
deflection results from
a more rare collision
in which the alpha
gets near to the
nucleus.
September 09
Modern Physics
Details of angular dependence
Theory:
Calculate trajectory
and deflection at
given impact
distance. Multiply
by probability of
hitting an annulus
of that distance.
It works!
September 09
Small deflection
Modern Physics
large deflection
Conclusion
The mass of an atom is concentrated in a
positively charged atomic “nucleus”.
The nuclear radius is roughly 10,000 times
smaller than the atomic radius.
September 09
Modern Physics
Problem with model
Imagine a solar model - light negatively charged
electrons orbiting a heavy positively charged
nucleus. The Coulomb force is proportional to 1/r2
just like the gravitational force so the orbits are
ellipses.
The electrons are accelerated so will radiate EM
waves, lose energy, spiral in towards the nucleus.
The time to spiral from ~10-10 m to 10-15 m may be
calculated to be of order 1 ns.
Atoms should collapse!! What stabilizes the atom?
September 09
Modern Physics
Questions of physics
Some questions are so simple to state!
What is the sky dark at night?
Why is it cold in the winter time?
Why does matter not collapse (forming a black
hole)?
What is light? What is matter for that matter?
Why are “things” the size they are?
September 09
Modern Physics
Stability of matter
Newtonian/Maxwellian physics predicts collapse.
Something keeps this from happening. (Quantum
mechanics)
September 09
Modern Physics
What light do atoms emit?
A prism may be used to separate the frequencies
in a mixture of light.
September 09
Modern Physics
Atomic emission spectra
Atoms do radiate
light, but the
spectrum is not
continuous. Each
element emits a
characteristic
spectrum of discrete
frequencies which
tell us something
about the electrons
within.
September 09
Modern Physics
Absorption spectra (Sun)
Atoms absorb
radiation at the
same frequencies
at which they
emit.
From signature
spectra, one can
deduce the kinds
of atoms in a
source like the
Sun!
September 09
Modern Physics
Hydrogen
Hydrogen is the
simplest atom just one electron
orbiting a single
proton. It should
hold the key to
atomic physics.
September 09
Modern Physics
Rydberg’s formula
The discrete wavelengths emitted or absorbed by
hydrogen fit a simple formula:
The subscripts I and f as we will see refer to initial and
final states of the electron.
September 09
Modern Physics
Spectral series
For a fixed final state, a series of wavelengths is
historically associated with a different investigator.
September 09
Modern Physics
Bohr’s model
F=ma permits circular orbit at any radius.
Guess angular momentum quantization only discrete radii allowed.
September 09
Modern Physics
Bohr model radii
In this picture only
certain orbits are
permitted.
The minimum radius
(n=1) is called the Bohr
radius.
This condition is called
the ground state.
September 09
Modern Physics
Bohr model energies
Given the radius we can find the kinetic energy
Given the radius we can find the potential energy
The total energy for a given n is
September 09
Modern Physics
Bohr model energies
Transitions between
states implies emitted
energy spectrum just as
observed:
September 09
Modern Physics
Example Bohr model energies
What wavelength will
excite monatomic
hydrogen from the ground
state (n=1) to the n=3
state?
September 09
Modern Physics
Example Bohr model energies
What wavelength will
excite (monatomic)
hydrogen from the ground
state (n=1) to the n=3
state?
September 09
Modern Physics
Franck-Hertz experiment
Photons are emitted when an electron in an
excited state transitions to a state of lower
energy.
Photons are absorbed and excite electrons
from lower energy to higher energy states.
Collisions can also produce quantum excitation.
September 09
Modern Physics
Franck-Hertz experiment
Bombard gaseous atoms with electrons.
September 09
Modern Physics
Franck-Hertz experiment
Current vs accelerating voltage
September 09
Modern Physics
Franck-Hertz experiment
When electron energy is sufficient to
excite an atom, accelerated electron
transfers energy to the atom, comes to
rest and proceeds onward. A stripe of
gas is excited and florescence light is
seen.
September 09
Modern Physics
Reduced mass effects
In classical physics, two bodies orbit the center of mass.
The solution is equivalent to that of one object orbiting a
fixed point but with a reduced mass. Careful
measurement reveals R should be calculated with the
reduced mass for electron and proton.
September 09
Modern Physics
Check on Bohr model
In deuterium, the nucleus is p=>pn and about twice as
heavy slightly changing.
In He+, the nucleus is ppnn and we need e2 => Ze2
=2e2 and a different reduced mass.
We learn Bohr’s model works for other hydrogen like
cases - he is on to something.
But what??
September 09
Modern Physics