Download Quantization of Matter

Lecture 1
Quantization of Matter
• Molecules are the smallest constituent of matter that preserve its
physical and chemical properties.
• A molecule can be further divided into atoms.
• An atom is made of a nucleus and electrons.
• A nucleus consists of nucleons (neutrons and protons).
• A nucleon may be composed of quarks (up, down, strange, charmed,
top, and bottom) and anti-quarks.
• Other particles: pions, muons, neutrinos, …
Quantization of Electric Charge
Chemical changes occur when an electric current is passed through a
solution, known as electrolysis.
By looking at the process quantitatively, Faraday discovered the
following:
• The mass of a substance liberated at an electrode is proportional to the
total electric charge that has passed through the solution.
• The mass of a substance liberated at an electrode is proportional to the
chemical equivalent of the substance (the mass of an element or a
group of elements which would displace 1 mole of atomic hydrogen).
Farady’s Law of Electrolysis
Faraday’s findings can be summarized
mathematically as:
M
where M is the total mass liberated, m is atomic or
molecular weight per mole, n is chemical valence,
Q is the electric charge passed through the solution,
and F is the constant of proportionality.
If there is a fundamental unit for electric charge, e, each ion
carries with it a charge q = ne, then we have Q = Nne, where
N is the total number of ions. Therefore,
F
 Nne
M
N

e
n
M 
Q
nF
Fundamental Unit of Electric Charge
where NA is Avogadro’s number
Specifically, Faraday found that to decompose 1 mole of
monovalent ions requires a total charge of 96,487 C being
passed through the solution.
Therefore, we have
F
96487
19
e


1.60

10
C
23
N A 6.02  10
Millikan’s Oil Drop Experiment
Schematics: a cross section of two parallel conducting plates
which are connected to a power supply. The top plate has a
pin hole in it, through which oil drops are sprayed.
Motion of Oil Drops in Air
Ignoring the buoyancy force, an oil drop is under the influence of only two
forces: gravity and frictional force due to air. The equation of motion is
we have
Let
dv
m  mg  kv
dt
dv
 dt
g k v
m
k
yg v
m
k
dy   dv
m
m dy

 dt
k y
k
ln y   t  ln C
m
y
k
 k 
 k 
  exp   t   g  v  C exp   t 
C
m
 m 
 m 
Terminal Velocity
From the initial conditions: t=0, v=0, we get C=g. Finally, we have
k 

 t
mg 
v
1 e m 

k 


It is easy to see that as
mg
t  , v 
k
terminal velocity
Effects of Buoyancy
The buoyant force on an oil drop is given by
Fb   aVg  ma g
where ra is the density of air, V is the volume of the oil drop, and ma is thus
the mass of the air displaced by the oil drop.
Therefore, the buoyancy effectively reduces the mass of the oil drop
by ma, i.e., m = mo - ma
In summary, the terminal velocity is reached when the frictional force is equal to
the effective weight (mg) of the oil drop, or when the net force is zero.
In the Presence of Electric Field
The oil drop may acquire static charge from the spray nozzle.
Assuming that it is negatively charged, it experiences a upward
electric force as soon as the power is turn on, as shown. If the
electric force is strong enough, the oil drop will slow down in
its downward motion, stop, turn around and accelerate upward.
It will quickly reach a
new terminal velocity
given by
Fe  mg  kv2
V
q  mg  kv2
d
d
In the Presence of Ionized Air
The air between the plates is ionized by X-rays or high-energy
radiation from radioactive substance passing through it. In this
case, the oil drop can acquire additional electric charge, which
disrupts the uniform motion, but, after a short time, a new
terminal velocity is reached by the drop when
V
 q  qn   mg  kv3
d
Therefore, the amount of charge acquired is
d
qn  k (v3  v2 )
V
Results
The up and down movement of an oil drop can be controlled by alternating
the voltage between the two plates. As a result, the oil drop can be held
between the plates for a long time for a series of measurements.
Millikan discovered that qn is always an integral multiple of
an “elementary” charge e, i.e.,
qn  ne
He correctly identified the elementary charge with the charge
of an “electron”, a constituent of atoms discovered by
J.J. Thomson about a decade earlier.