Biomedical Engineering Reference
In-Depth Information
2.2
The Rutherford Nuclear Atom
The existence of alpha, beta, and gamma rays was known by 1900. With the dis-
covery of these different kinds of radiation came their use as probes to study the
structure of matter itself.
Rutherford and his students, Geiger and Marsden, investigated the penetration
of alpha particles through matter. Because the range of these particles is small,
an energetic source and thin layers of material were employed. In one set of ex-
periments, 7.69-MeV collimated alpha particles from
21
84
Po (RaC
) were directed at
a
6
10
-5
cm thick gold foil. The relative number of particles leaving the foil at
various angles with respect to the incident beam could be observed through a mi-
croscope on a scintillation screen. While most of the alpha particles passed through
the foil with only slight deviation from their original direction, an occasional par-
ticle was scattered through a large angle, even backwards from the foil. About 1
in 8000 was deflected more than 90
◦
. An enormously strong electric or magnetic
field would be required to reverse the direction of the fast and relatively massive
alpha particle. (In 1909 Rutherford conclusively established that alpha particles are
doubly charged helium ions.) “It was about as credible as if you had fired a 15-in.
shell at a piece of tissue paper and it came back and hit you,” said Rutherford of
this surprising discovery. He reasoned that the large-angle deflection of some alpha
particles was evidence for the existence of a very small and massive nucleus, which
was also the seat of the positive charge of an atom. The rare scattering of an alpha
particle through a large angle could then be explained by the large repulsive force it
experienced when it approached the tiny nucleus of a single atom almost head-on.
Furthermore, the light electrons in an atom must move rapidly about the nucleus,
filling the volume occupied by the atom. Indeed, atoms must be mostly empty
space, allowing the majority of alpha particles to pass right through a foil with little
or no scattering. Following these ideas, Rutherford calculated the distribution of
scattering angles for the alpha particles and obtained quantitative agreement with
the experimental data. In contrast to the plum pudding model. Rutherford's atom
is sometimes called a planetary model, in analogy with the solar system.
Today we know that the radius of the nucleus of an atom of atomic mass number
A
is given approximately by the formula
×
R
=
1.3
A
1/3
× 10
-15
m.
(2.2)
The radius of the gold nucleus is
1.3(197)
1/3
= 7.56 × 10
-15
m. The atomic
radius of gold is
1.79 × 10
-10
m. The ratio of the two radii is
(7.56 × 10
-15
/1.79 ×
10
-10
)
× 10
-15
10
-5
. In physical extent, the massive nucleus is only a tiny speck at
the center of the atom.
=
4.22
×
