Atomic structure

•Atomic structure

•Black body Radiation and Photoelectric Effect gave the impulse to understand the nature of light

•However, there was no understanding on how electrons “exist” inside matter

–It was known that atoms that form matter contain electrons (Thompson, 1897) and that atoms are neutral

Thomson Model

–Electrons are embedded within spherically distributed, positive charge (so-called “plum pudding” model)

–Both the positive charge and the mass of the atom would be more or less uniformly distributed over its size

•Approximately 10-10 meters across = 1 Å = 0.1 nm

Problems with Thomson’s Model

•How does the atom emit radiation?

•This model soon came into conflict with experiments by Rutherford

The Rutherford Experiments

•Rutherford discovered α (alpha)-particles

–α-particles are the nuclei of helium atoms, which were

products of nuclear disintegration

–He used α-particles in various studies

•In 1909, he with co-workers (Hans Geiger and Ernest

Marsden) experimented with streams of alpha particles

passing through a thin gold foil

•The foil thickness was ~ 8.6 x 10-6 cm

–The foil was thin and so was supported on a glass plate

•The plate itself was found to be transparent to the alpha particles

•Since atoms have no overall electrical charge (atoms 

are neutral), there must be just enough negatively

charged particles outside the nucleus to just balance 

the positively-charged nucleus

Therefore,

The Rutherford's experiment suggested that the atom

consists of mostly empty space with a very small

positively-charged nucleus, outside which are just

enough negative charges to equal the positive charge in

the nucleus

Since the electrons do not crash into the nucleus but

exist in stable atoms, this suggests a planetary model

with negatively charged electrons circulating around a

positive core

Estimate of Nuclear Cross Section 

•Approximately one in 104 a particles with energies of 

~ 107 eV are scattered backward from a one micron 

thick sheet of metal foil

•If atomic spacing is ~ 1 A, then there are 104 atomic 

layers so the probability of scattering by a single layers

 is 10-8

•This implies the nuclear cross section is one part in 

108 of the atomic cross section

•Since the area goes as the square of the radius the

 nuclear radius is smaller than atomic radius by a factor

 of 10-4

•Since the atomic diameter is ~ 1 A, the nuclear 

diameter is ~ 10-4 A

•The model of a small positively charge nuclear core 

was confirmed by a comparison with the angular 

distribution to scattered a-particles

•The incident a-particles are assumed to have a 

uniform distribution in space. Initial trajectories that are 

headed towards the nuclei of atoms in the foil with 

random separations from the nearest nuclear core

•Full trajectory calculated for each distance of the

 trajectory line from the center of the nearest nucleus to

 give the scattering angle

•From the distribution of distances of the a-particles 

from the positive core calculate distribution of 

scattering angle

•Agreement found with measured scattering angle

 distribution

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