WHY CAN'T WE SEE ATOMS?
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“seeing an object”
 = detecting light that has been reflected off the
object's surface
light = electromagnetic wave;
“visible light”= those electromagnetic waves that our
eyes can detect
“wavelength” of e.m. wave (distance between two
successive crests) determines “color” of light
wave hardly influenced by object if size of object is
much smaller than wavelength
wavelength of visible light:
between 410-7 m (violet) and 7 10-7 m (red);
diameter of atoms: 10-10 m
generalize meaning of seeing:
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seeing is to detect effect due to the presence of an
object
quantum theory  “particle waves”,
with wavelength 1/(m v)
use accelerated (charged) particles as probe, can
“tune” wavelength by choosing mass m and changing
velocity v
this method is used in electron microscope, as well as in
“scattering experiments” in nuclear and particle physics
WHAT IS INSIDE AN ATOM?
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THOMSON'S MODEL OF ATOM
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(“RAISIN CAKE MODEL”):
 atom = sphere of positive charge
(diameter 10-10 m),
 with electrons embedded in it, evenly
distributed (like raisins in cake)
Geiger & Marsden’s SCATTERING EXPERIMENT:
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(Geiger, Marsden, 1906 - 1911) (interpreted by
Rutherford, 1911)
get particles from radioactive source
make “beam” of particles using “collimators” (lead
plates with holes in them, holes aligned in straight
line)
bombard foils of gold, silver, copper with beam
measure scattering angles of particles with
scintillating screen (ZnS) .
Geiger, Marsden, Rutherford expt.
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result:
 most particles only slightly deflected (i.e. by
small angles), but some by large angles - even
backward
 measured angular distribution of scattered
particles did not agree with expectations from
Thomson model (only small angles expected),
 but did agree with that expected from
scattering on small, dense positively charged
nucleus with diameter < 10-14 m, surrounded by
electrons at 10-10 m
Rutherford model
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RUTHERFORD MODEL OF ATOM:
(“planetary model of atom”)
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problem with Rutherford atom:
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positive charge concentrated in nucleus (<10-14 m);
negative electrons in orbit around nucleus at
distance 10-10 m;
electrons bound to nucleus by Coulomb force.
electron in orbit around nucleus is accelerated
(centripetal acceleration to change direction of
velocity);
according to theory of electromagnetism
(Maxwell's equations), accelerated electron emits
electromagnetic radiation (frequency = revolution
frequency);
electron loses energy by radiation  orbit decays,
changing revolution frequency  continuous
emission spectrum (no line spectra), and atoms
would be unstable (lifetime  10-10 s )
 we would not exist to think about this!!
Bohr model of hydrogen (Niels Bohr, 1913)
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Bohr model is radical modification of Rutherford
model; discrete line spectrum attributed to
“quantum effect”;
electron in orbit around nucleus, but not all orbits
allowed;
three basic assumptions:
 1. angular momentum is quantized
L = n·(h/2) = n ·ħ, n = 1,2,3,...
electron can only be in discrete specific
orbits with particular radii
 discrete energy levels
 2. electron does not radiate when in one of the
allowed levels, or “states”
 3. radiation is only emitted when electron makes
“transition” between states,
transition also called “quantum jump” or
“quantum leap”
from these assumptions, can calculate radii of
allowed orbits and corresponding energy levels:
radii of allowed orbits:
rn = a0 n2 n = 1,2,3,….,
a0 = 0.53 x 10-10 m = “Bohr radius”
n = “principal quantum number”
allowed energy levels:
En = - E0 /n2 , E0 = “Rydberg energy”
note: energy is negative, indicating that electron is
in a “potential well”; energy is = 0 at top of well, i.e.
for n = , at infinite distance from the nucleus.
Ground state and excited states
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ground state = lowest energy state, n = 1;
this is where electron is under normal circumstances;
electron is “at bottom of potential well”;
energy needed to get it out of the well = “binding
energy”;
binding energy of ground state electron = E0 =
energy to move electron away from the
nucleus (to infinity), i.e. to “liberate” electron;
this energy also called “ionization energy”
excited states = states with n > 1
excitation = moving to higher state
de-excitation = moving to lower state
energy unit eV = “electron volt” = energy acquired by an
electron when it is accelerated through electric
potential of 1 Volt; electron volt is energy unit
commonly used in atomic and nuclear physics;
1 eV = 1.6 x 10-19 J
relation between
energy and wavelength:
E = h f = hc/ ,
hc = 1.24 x 10-6 eV m
Excitation and de-excitation
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PROCESSES FOR EXCITATION:
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gain energy by collision with other atoms, molecules
or stray electrons; kinetic energy of collision
partners converted into internal energy of the
atom; kinetic
energy comes from heating or discharge;
absorb passing photon of appropriate energy.
DE-EXCITATION:
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spontaneous de-excitation with emission of photon
which carries energy = difference of the two
energy levels;
typically, lifetime of excited states is  10-8 s
(compare to revolution period of  10-16 s )
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Excitation:
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states of electron in hydrogen atom:
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MICROWAVE COOKING
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water molecule has rotational energy levels close
together  small energy difference  can absorb
microwaves;
microwaves: wavelength  3cm, frequency  10GHz =
1010 Hz; energy of photon = h f  4.13x10-5 eV
it is water content that is critical in microwave
cooking; most dishes and containers do not absorb
microwaves  are not heated by them, but get hot
from hot food.
IONIZATION:
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if energy given to electron > binding energy, the atom
is ionized, i.e. electron leaves atom; surplus energy
becomes kinetic energy of freed electron.
this is what happens, e.g. in photoelectric effect
ionizing effect of charged particles exploited in
particle detectors (e.g. Geiger counter)
aurora borealis, aurora australis:
cosmic rays from sun captured in earth’s magnetic
field, channeled towards poles;
ionization/excitation of air caused by charged
particles, followed by recombination/de-excitation;
Matter waves
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Louis de Broglie (1925):
any moving particle has wavelength associated
with it:  = h/p = h/(mv)
example: electron in atom has   10-10 m;
car (1000 kg) at 60mph has   10-38 m;
wave effects manifest themselves only in
interaction with things of size comparable to
wavelength  we do not notice wave aspect of our
cars.
note: Bohr's quantization condition for angular
momentum is identical to requirement that integer
number of electron wavelengths fit into
circumference of orbit.
experimental verification of de Broglie's matter
waves:
 beam of electrons scattered by crystal lattice
shows diffraction pattern (crystal lattice acts
like array of slits);
experiment done by Davisson and Germer (1927)
 Electron microscope
QUANTUM MECHANICS
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= new kind of physics based on synthesis of dual
nature of waves and particles;
developed in 1920's and 1930's.
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Schrödinger equation: (Erwin Schrödinger, 1925)
 is a differential equation for matter waves;
basically a formulation of energy conservation.
 its solution called “wave function”, usually
denoted by ;
 |(x)|2 gives the probability of finding the
particle at x;
 applied to the hydrogen atom, the Schrödinger
equation gives the same energy levels as those
obtained from the Bohr model;
 the most probable orbits are those predicted
by the Bohr model;
 but probability instead of Newtonian
certainty!
Uncertainty principle: (Werner Heisenberg, 1925)
It is impossible to simultaneously know a particle's
exact position and momentum (or velocity)
p x  ħ = h/(2)
(remember h is a very small quantity:
h = 6.63 x 10-34 J  s = 4.14 x 10-15 eV)
(note that here p means “uncertainty”
in our knowledge of the momentum p)
note that there are many such uncertainty relations
in quantum mechanics, for any pair of
“incompatible” observables.