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Atomic World – Rutherford’s Atomic Model
Part 1: Rutherford’s Atomic Model
Outline
Atomic (microscopic) Nature of Matters - Early Evidences
Electric Charge of Electron – Millikan’s Oil Drop Experiment
Thomson’s ‘Plum Pudding’ Model of Atom
Rutherford’s Scattering Experiment
Rutherford’s Atomic Model
Brief History of Atomic Nature of Matters
John Dalton and Modern Atomic Theory (1808)
Cathode Ray (William Crookes, 1879)
X-Ray (Roentgen, 1895) and Radioactivity (1896)
e/m Determination (J.J. Thomson, 1897)
J. J. Thomson’s ‘Plum Pudding’ (1897)
The Particle (Quanta) Nature of Light (Planck, 1900)
Einstein’s Theory of Photoelectric Effect (Einstein, 1905)
Measurement of Electron Charge (Millikan, 1909)
Determination of Avogadro’s Number (Perrin, 1909)
Discovery of The Atomic Nucleus (Rutherford, 1911)
Bohr’s Atomic Model (Bohr, 1913)
Atomic Theories (400 BC - 1900 AD)
Democritus of Abdera (460-370 B.C.):
He is the first person who suggested the idea that matters
are made of different elements. They consisted of empty
space and an infinite number of atoms (a-tomos, meaning
"uncuttable"). These atoms were eternal and indivisible,
and moved in the void of space. There were no
experimental data at that time. Nevertheless, roughly
about 90 elements were discovered by 1900.
Figure 1.1 Democritus of Abdera
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Atomic World – Rutherford’s Atomic Model
John Dalton (1808):
John Dalton was a chemist who introduced the idea of
the Law of Definite Proportions. This was the first idea
that matters can be added to form matters,
for example, (3g of X) + (4g of Y) produces 7g of XY.
Though Dalton suggested the idea of atomic world, but
he did not prove - the ‘atomic’ nature of matter.
Figure 1.2 John Dalton
Mysterious Rays using Crookes Tubes:
Sir William Crookes worked with vacuum tubes which consisted of electrodes.
These Crookes tubes are simply evacuated glass tubes with electrodes to which a
voltage can be applied. In 1879, he discovered emission from the cathode of such
a tube and showed that this emission could be blocked by an object and form
shadow on the other side of the tube. He named this ‘cathode ray’ and believed
that these were a stream of particles of some sort.
cathode
anode
Figure 1.3 Sir William Crookes
Figure 1.4 Crookes Tube
Discovery of X-Ray (W. C. Roentgen, 1895):
Roentgen was using a simple Crookes tube to study this ‘cathode ray’, and noticed an
object across the room (paper coated with barium platinocyanide) began to glow. He
did not know why, but was able to reproduce the effect. When the announcement was
finally made, he still did not know what it was – so he named it X-ray. In recognition
of the extraordinary services he had rendered by the discovery of the remarkable rays
subsequently named after him, Röntgen was awarded the Nobel Prize in Physics
1901.
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Atomic World – Rutherford’s Atomic Model
Figure 1.5 Wilhelm Conrad Roentgen
Figure 1.6 Laboratory of Wilhelm Conrad Roentgen
Figure 1.7 The famous radiographs made by Roentgen on
22 December 1895 and on 23 January 1896. Noted that the
radiographs have already much improved in resolution.
J.J. Thomson and the electron (1897):
First experiment: Magnetic field was used to bend the ‘cathode ray’ into the
electrometer (which detected the charge). This showed that the charge could not
be separated from the ‘ray’. Second experiment: He showed that the ray could be
deflected by electric field – but only after the tube had been very well evacuated
by pumps.
Figure 1.8 J.J. Thomson in the Cavendish Lab
Figure 1.9 Thomson’s apparatus in the first experiment
Figure 1.10 Thomson’s apparatus in the second experiment
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Atomic World – Rutherford’s Atomic Model
Thomson’s proposals
1. Cathode rays are charged particles (which he called
2.
3.
"corpuscles“, and we now call electrons).
These electrons are constituents of the atom. He tried
different gases in the tube and different cathode materials,
but obtained the same e/m ratio: there is only one kind of
electron in all atoms
The e/me ratio for ions have been known (from
electrolysis) and it is 2000 times more than that for
hydrogen ions, and Thomson reasoned correctly that the
electron has smaller mass.
Figure 1.11 Joseph John Thomson
He got the Nobel Prize in Physics 1906.
He also proposed the ‘Plum Pudding’ or ‘raisin cake’ atomic model, in which
electrons are the raisins in the positively charged cake. There will be more discussions
on this topic later.
The Discovery of Radioactivity
Henri Becquerel (1896):
X-Ray had just been discovered from the fluorescence
produced and Henri Becquerel wanted to study this
new X-ray.
The fluorescence was obtained from some minerals
after exposed to sun light.
He chose a uranium compound, and was ready to
charge it on 26th and 27th of February under sunlight. Figure 1.12 Henri Becquerel
But both days, Paris was cloudy. He put the
compound in a drawer, to wait for sunny days, next to a pack of photographic
plates for a few days. He checked the plates to make sure everything was fine
before performing his experiment, and to his amazement, the plates showed the
image of the uranium compound. Natural radioactivity was discovered! This
new radiation was later shown by Rutherford that it consists of three components:
α, β and γ.
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Atomic World – Rutherford’s Atomic Model
Figure 1.13 Image of Becquerel's photographic plate which was fogged by exposure to radiation from
uranium salts. The shadow of a metal Maltese Cross placed between the plate and the uranium salts is
clearly visible.
The Curies: Pierre & Marie
Instead of making these uranium compounds act upon photographic plates, they
determined the intensity of the radiation by measuring the conductivity of the air
exposed under the radiation. Marie Curie hypothesized that emission of these
mysterious rays (radiations) from uranium compounds is an atomic property of
the element uranium–an intrinsic property built into the structure of uranium
atoms.
Figure 1.14 This device for precise electrical
measurement, invented by Pierre Curie and his
brother Jacques
Figure 1.15 The Curies: Pierre & Marie
Discovery of Radium
The Curies needed to make pure samples using chemical processes. Only two to three
decigrams of radium was extracted from seven tons of pitch-blende ore. Heat
liberation was found in solid salt of radium - one hundred calories per hour per gram.
Antoine Henri Becquerel, Pierre Curie, and Marie Curie – Nobel Prize 1903
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Atomic World – Rutherford’s Atomic Model
Three types of radiation coming out of Radium
Rutherford showed that there were three different kinds of ray in radioactivity. By
carefully observing on a fluorescent screen the paths of the particles through a
magnetic field, he was able to determine the charges associated with the three kinds of
ray. Rutherford called the positive ray alpha, beta for the negative ray, and gamma for
the neutral ray.
Figure 1.16 Ernest Rutherford
Figure 1.17 Three types of radiation
Millikan Oil Drop Experiment (1909)
J.J. Thomson had determined the e/me ratio – which
does not depend on materials used. But this did not
prove the existence of electron. There could be a
range of different sizes of electrons and still have the
same e/me ratio. To determine the charge, the
scientists experimented with measuring the motion of
water droplets ‘charged’ or ionized by X-rays in an
electric field – but were unable to get good results
Figure 1.18 Robert Andrews Millikan
due to difficulties such as evaporation of the droplets.
Robert Millikan’s experiment overcame many of those difficulties. The key advance
was the use of oil instead of water - the idea occurred to him on a train trip that
lubrication oil does not evaporate very fast. Millikan was then able to watch single oil
droplet for hours, put on and take away charges by X-rays, and measure the change in
the velocity of a single oil droplet.
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Atomic World – Rutherford’s Atomic Model
Basic principle of Oil Drop Experiment
Unbalanced force on a droplet with mass M and charge q in vacuum under an E-field
is
F = qE − Mg
When the droplet is stationary, i.e. F = 0,
qE = Mg
Knowing M and E, one can get q.
To find M of the droplet, one can use the Stokes’ Law which gives the viscous force
on a moving sphere, and measure the terminal velocity v of the droplet in air in the
absence of the E-field (viscosity η ).
4 3
πr ρg
2 r 2 ρg
F
Mg
Terminal speed v =
=
=3
=
6πrη 6πrη
6πrη
9η
This gives the radius r of the droplet, and hence M knowing the density ρ.
Figure 1.19 Millikan's setup for the oil drop experiment
Conclusion
The Millikan oil-drop experiment was far superior to previous determinations of the
charge of an electron. Where other workers had attempted to measure the quantity by
observing the effect of an electric field on a cloud of water droplets, Millikan used
single drops, first of water and then, when he found these evaporating, of oil. His
measurement was off by only 0.5%, and most of this error was due to his adoption of
a plausible but wrong value for the viscosity of air. The experiment had broader
significance than a simple refinement of a number. Millikan emphasized that the very
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Atomic World – Rutherford’s Atomic Model
nature of his data refuted conclusively the minority of scientists who still held that
electrons (and perhaps atoms too) were not necessarily fundamental, discrete particles.
And he provided a value for the electronic charge which, when inserted in Niels
Bohr's theoretical formula for the hydrogen spectrum, accurately gave the Rydberg
constant—the first and most convincing proof of Bohr's quantum theory of the atom.
Thomson and Millikan: electrons have definite charge and mass
Atoms contain negatively charged electrons. Electron has mass about 2000 times less
than hydrogen ion, but the (negative) electron charge is equal to the (positive) charge
of the ion in magnitude. Atoms are neutral. There must be positive charge in them.
How is the positive charge distributed within the atom? And what is the distribution
of the mass about?
Thomson’s ‘Plum Pudding’ or ‘Raisin Cake’ Model of the atom
Figure 1.20 Thomson’s “Plum Pudding” or “Raisin Cake” Model of the atom
Raisins are the electrons. Positive charge and mass distributed uniformly about the
atom (‘the bread’) and the size of the ‘bread’ is about 10-10m (atomic size).
Rutherford asked his students to useαparticles from radium as projectiles to probe
this ‘raisin cake’. The sample used was a gold foil (which can be very thin).
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Atomic World – Rutherford’s Atomic Model
Rutherford’s expectation and the surprise
Radium
Gold foil
Figure 1.21 Rutherford’s technique for observing the scattering of alpha particles from a thin foil target.
The source is a naturally occurring radioactive substance, such as radium.
The positively charged α particles have 7.7 MeV of energy, and 8000 times more
massive than the electrons (‘the raisins’) - they will not be deflected by the electrons
or the “bread” (uniformly distributed positive charges) as suggested in the Thomson’s
model. But before going through the trouble of slowing down the α particles,
Rutherford asked his students to try out the setup, fully expecting that the beam would
go right through the gold foil with very little scattering. They found a small number of
those 7.7 MeV α particles deflected by very large angles - even 180 degrees!
The Scattering of α and β Particles by Matter and the Structure of the Atom
(E. Rutherford, F.R.S.* Philosophical Magazine (1911))
Rutherford realized that such large deflection could not possibly be resulted from a
single scattering in the Thomson’s model. However, he was able to show that the
probability of multiple scatterings was far too small to explain the observations.
Since electric field is proportional to 1/r2, such high field requires concentration of
charge to a very small r. The positive charge CANNOT be the ‘bread’ surrounding the
electrons - all the charge must be concentrated to a very small NUCLEUS. How
small?
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Atomic World – Rutherford’s Atomic Model
Rutherford Scattering: How Small is the nucleus?
Figure 1.22 If none of the alpha particles penetrates into the nucleus, r > R for all points on all orbits.
The closest approach rmin occurs in a head-on collision.
Let’s try a simple calculation:
Assume deflection by electrons in the atom is very small compared to the positively
charged (Z=79) nucleus. And also the α particles, charge = 2e, are deflected before
they can penetrate the target nuclei.
Using conservation of energy:
Rutherford Scattering
1 2 Ze 2 2 Zke 2
=
4πε r
r
2
ke = 1.44eV ⋅ nm = 1.44 MeV ⋅ fm
U=
2 Zke 2
~ 30 fm
K
(K = 7.7MeV, K.E. of the α particle)
R ≥ rmin =
f stands for ‘femto’ 10-15 (Atomic size ~ 10-10 m, and gold nucleus ~ 8 fm)
Rutherford Scattering
The Coulomb repulsion of the nucleus:
2 Zke 2
r2
It can be shown that the impact parameter b is
F=
given by:
Zke 2
b=
E tan (θ / 2)
Figure 1.23 Trajectory of the alpha particles in
the Coulomb field of a nucleus. The initial and
final momenta are labeled pi and pf.
Note that all particles with impact parameter less than b will be deflected more than θ
and E denotes the energy of the incident alpha particles.
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Atomic World – Rutherford’s Atomic Model
For a particle beam with cross-sectional area A and total number of particles N:
Number scattered through θ or more by one gold atom = N
πb 2
A
Figure 1.24 (a) A particle with impact parameter b is deflected by an angle θ; all those particles that
impinge on the circle of area πb2 are deflected by more than θ. (b) The cross-sectional area of the
whole beam is A; the volume of target interested by the beam is At.
If the target gold foil has thickness t and contains n atoms in unit volume:
Number of target atoms encountered = nAt
Total number of a particles scattered through θ or more
Nπb 2
nAt = πNntb 2
A
Thus the number of particles per unit area at distance s from the foil emerging
between θ and θ + dθ can be obtained by differentiating N sc (> θ ) :
N sc (≥ θ ) =
n sc (θ ) =
N sc (θ , θ + δθ ) Nnt Zke 2 2
1
= 2(
)
2
4
E
2πs sin θδθ
4s
sin (θ / 2)
This important result is called the Rutherford formula.
Figure 1.25 Gigerm and Marsden measured the flux of scattered alpha particles at different angles.
Their measurements fit Rutherford’s predicted 1/sin4(θ/2) behavior beautifully.
It was verified by Geiger and Marsden in 1913.
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Atomic World – Rutherford’s Atomic Model
Scattering of α Particles by Matters
Figure 1.26 Alpha particles (from R) scatter off the foil
(F). The microscope (M) is rotated around the
cylindrical box (B) to count scattering at any angle
“It was quite the most incredible event that ever happened to me in my life. It was as
incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back
and hit you.”----- Rutherford
Structure of Nucleon
Rutherford explained his astonishing results by developing a new atomic model, one
that assumed the positive charge in the atom was concentrated in a region that was
small relative to the size of the atom. He called this concentration of positive charge
the nucleus of the atom. Any electrons belonging to the atom were assumed to be in
the relatively large volume outside the nucleus. To explain why these electrons were
not pulled into the nucleus by the attractive electric force, Rutherford modeled them
as moving in orbits around the nucleus in the same manner as the planets orbit the Sun.
For this reason, this model is often referred to as the planetary model of the atom.
In Rutherford’s scattering experiment, he kept seeing that the atomic number Z
(number of protons in the nucleus, equivalent to the positive charge of the atom) was
less than the atomic mass A (average mass of the atom) implying something besides
the protons in the nucleus were adding to the mass. He put out the idea that there
could be a different kind of particle with mass but no charge. He called it a neutron.
Rutherford’s former student James Chadwick, using a refined particle detection, was
able to determine that neutron did exist and its mass was about 0.1 percent more than
that of proton. In 1935 Chadwick received the Nobel Prize for his discovery.
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Atomic World – Rutherford’s Atomic Model
Figure 1.27 Ernest Rutherford
Figure 1.28 James Chadwick
Limitations of Rutherford’s atomic model
Two basic difficulties exist with Rutherford’s planetary model. The first difficulty is
that an atom emits (and absorbs) certain characteristic frequencies of electromagnetic
radiation and no others. The Rutherford model cannot explain this phenomenon. The
second difficulty is that the electrons in Rutherford’s model are undergoing a
centripetal acceleration. According to Maxwell’s theory of electromagnetism,
centripetally accelerated charges revolving with frequency f should radiate
electromagnetic waves of frequency f. Unfortunately, this classical model leads to a
prediction of self-destruction when applied to the atom. As the electron radiates,
energy is carried away from the atom, the radius of the electron’s orbit steadily
decreases, and its frequency of revolution increases. This would lead to an
ever-increasing frequency of emitted radiation and an ultimate collapse of the atom as
the electron plunges into the nucleus.
Figure 1.29 The electromagnetic radiation of an orbiting
electron in the planetary model of the atom will cause the
electron to spiral inward until it crashes into the nucleus.
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Atomic World – Rutherford’s Atomic Model
Scattering in particle physics
The scattering experiment of Rutherford certainly identified the nuclei and hence
provided the picture for an atom. Scattering experiment in general involves the
collision between a target and an impacting particle, and the study of resulted particles.
In this sense, Rutherford's experiment was an early stage particle physics and many
new particles were discovered using the scattering / collision technique.
In particle physics, scattering refers to the deflection of subatomic particles. It is a
core process in many experiments. In scattering experiments, a target is bombarded
with a beam of particles (typically can be electrons, protons, neutrons or even quarks),
and the number of particles emerging in various directions are then measured. This
distribution reveals information about the interaction that takes place between the
target and the scattered particle.
Depending on the degree of interaction between the incident particle and the target,
the scattering process can be classified as elastic, inelastic or deeply inelastic. In an
elastic scattering process (e.g. Rutherford scattering and Rayleigh scattering), the
incident and target particles are left intact and only their momenta may be changed. In
an inelastic scattering process (e.g. Compton scattering), the target particle may be
excited. For example, if a nucleus is bombarded by neutrons, it may be excited to
demonstrate nuclear resonance. In a deep inelastic scattering process (e.g. the first
convincing evidence of the reality of quarks), the target (and sometimes the incident
particle as well) may be destroyed and completely new particles may be created.
Modern particle physics research focuses on the finding and studying of subatomic
particles, which have simpler structure than atoms. These include atomic constituents
such as electrons, protons, and neutrons (protons and neutrons are actually composite
particles, made up of quarks). Besides, a wide range of exotic particles were
discovered in radioactive and scattering processes, such as photons, neutrinos and
muons.
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Atomic World – Rutherford’s Atomic Model
Summary
Atoms:
Electrons + Nucleus (Protons + Neutrons)
Atomic Radius:
~ 10-10 m
Nucleus:
~ < 30 fm
Mass of Hydrogen Atom:
1.6 x 10-27 kg or 940 MeV/c2
Electrons:
1
Charge
-1.6 x 10-19 C
Mass
9.1 x10-31 kg or 0.5 MeV/c2
H
238
U
#e
#p
#n
Z
A
Hydrogen
1
1
0
1
1
Uranium
92
92
146
92
238
References
Brief History of Atomic Nature of Matters
http://molaire1.club.fr/e_histoire.html
Democritus of Abdera
http://www.livius.org/de-dh/democritus/democritus.html
John Dalton
http://www.chemheritage.org/classroom/chemach/periodic/dalton.html
Sir William Crookes
http://members.chello.nl/~h.dijkstra19/page7.html
Wilhelm Conrad Roentgen
http://www.xray.hmc.psu.edu/rci/ss1/ss1_2.html
Joseph John Thomson
http://www.aip.org/history/electron/jj1897.htm#apparatus
http://www.aip.org/history/electron/jjsound.htm
Henri Becquerel
http://www.mlahanas.de/Physics/Bios/HenriBecquerel.html
The Curies: Pierre & Marie
http://www.aip.org/history/curie/contents.htm
Ernest Rutherford
http://nobelprize.org/nobel_prizes/chemistry/laureates/1908/rutherford-bio.html
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Atomic World – Rutherford’s Atomic Model
Robert Andrews Millikan
http://nobelprize.org/nobel_prizes/physics/laureates/1923/millikan-bio.html
http://www.aip.org/history/gap/Millikan/Millikan.html
James Chadwick
http://nobelprize.org/nobel_prizes/physics/laureates/1935/chadwick-bio.html
Milikan’s Oil Drop Experiment
http://www68.pair.com/willisb/millikan/experiment.html
The Isolation of an Ion, a Precision Measurement of its Charge, and the Correction of
Stokes' Law
http://nss.phys.ust.hk/pdf/millikan.pdf
Geiger and Marsden's Apparatus for Scattering Experiment
http://www-outreach.phy.cam.ac.uk/camphy/nucleus/nucleus_exp.htm
A Rutherford Scattering Applet
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/rutherford/
rutherford.html
Determining the electron charge to mass ratio (e/me)
http://nss.phys.ust.hk/lab/EMRatio.pdf
Resources for the History of Physics & Allied Fields
http://www.aip.org/history/web-link.htm
Institute of Physics
http://www.iop.org/IOP/Groups/
Wikipedia - Atomic Physics
http://en.wikipedia.org/wiki/Atomic_physics
Chemical Achievers - The Human Face of the Chemical Sciences
http://www.chemheritage.org/classroom/chemach/periodic/dalton.html
Wikipedia - Particle Physics
http://en.wikipedia.org/wiki/High_energy_physics
Wikipedia - Scattering
http://en.wikipedia.org/wiki/Scattering
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