Introduction to Quantum Ideas
49
For Z = 1 and a frequency ν ≈ 5 × 10
14
s
-1
corresponding to a wavelength of
λ = 6000 Å, one gets R 0 ≈ 3 Å which is comparable to the size of the atom and
therefore can be taken as a support for the Thomson model. A suitable
arrangement of the electrons in a series of rings, can also explain the existence
of homologue series such as Na, K, Rb, etc. which have similar properties.
However, the model is totally inconsistent with the experimental observations of
the scattering of a particles by thin metal foils, and had to be discarded. Now, it
is only of historical interest.
2.6 NUCLEAR MODEL OF THE ATOM
The distribution of charge and mass in an atom can be investigated by the
scattering of charged particles by the atom. Such an investigation was carried
out by Rutherford and his collaborators.
It was observed by Geiger and Marsden (1909) that in the scattering of
α particles (doubly ionised
4
He) by the atoms in a thin metal foil, though most of
the α particles emerged without much deviation, some of them were scattered
through large angles (some close to 180 degrees). The number of such events
was at least 10
4
larger than the number expected from the multiple scatterings
by the Thomson atoms with uniform positive charge distribution. Nor can these
large deflections be caused by the electrons in the atoms, since their mass is
very small. From an analysis of the data, Rutherford came to the conclusion that
the large deflections are caused by the strong electric field associated with a
large mass concentrated in a small volume. On the basis of this conclusion,
Rutherford proposed (1911) a nuclear model of the atom, which is the first
authentic model of the modern understanding of the atom.
Rutherford’s model of the atom consists of a nucleus of positive charge
Ze (Z is the atomic number), which carries most of the mass of the atom and is
concentrated in a very small region of radius less than 10
–14
m. Moving around
the nucleus are Z electrons at a distance from the nucleus roughly equal to the
size of the atom, i.e., 10
–10
m. The explanation of the α-particle scattering is
that most of the α particles go through the atom with only a slight deflection
except when they encounter the strong field due to the massive nucleus in
which case they undergo a large deflection. The detailed predictions of the
calculations based on this model are in very good agreement with the experimental
observations.
Consider the scattering of an α particle by a thin metal foil. Let the cross
sectional area of the beam be A. Then the total number of atoms which scatter
the α particles is
n = ρ At
(2.50)
where ρ is the number of atoms per unit volume, and t is the thickness of the
foil. For each atom, let the incoming α particles in the impact parameter range
49
For Z = 1 and a frequency ν ≈ 5 × 10
14
s
-1
corresponding to a wavelength of
λ = 6000 Å, one gets R 0 ≈ 3 Å which is comparable to the size of the atom and
therefore can be taken as a support for the Thomson model. A suitable
arrangement of the electrons in a series of rings, can also explain the existence
of homologue series such as Na, K, Rb, etc. which have similar properties.
However, the model is totally inconsistent with the experimental observations of
the scattering of a particles by thin metal foils, and had to be discarded. Now, it
is only of historical interest.
2.6 NUCLEAR MODEL OF THE ATOM
The distribution of charge and mass in an atom can be investigated by the
scattering of charged particles by the atom. Such an investigation was carried
out by Rutherford and his collaborators.
It was observed by Geiger and Marsden (1909) that in the scattering of
α particles (doubly ionised
4
He) by the atoms in a thin metal foil, though most of
the α particles emerged without much deviation, some of them were scattered
through large angles (some close to 180 degrees). The number of such events
was at least 10
4
larger than the number expected from the multiple scatterings
by the Thomson atoms with uniform positive charge distribution. Nor can these
large deflections be caused by the electrons in the atoms, since their mass is
very small. From an analysis of the data, Rutherford came to the conclusion that
the large deflections are caused by the strong electric field associated with a
large mass concentrated in a small volume. On the basis of this conclusion,
Rutherford proposed (1911) a nuclear model of the atom, which is the first
authentic model of the modern understanding of the atom.
Rutherford’s model of the atom consists of a nucleus of positive charge
Ze (Z is the atomic number), which carries most of the mass of the atom and is
concentrated in a very small region of radius less than 10
–14
m. Moving around
the nucleus are Z electrons at a distance from the nucleus roughly equal to the
size of the atom, i.e., 10
–10
m. The explanation of the α-particle scattering is
that most of the α particles go through the atom with only a slight deflection
except when they encounter the strong field due to the massive nucleus in
which case they undergo a large deflection. The detailed predictions of the
calculations based on this model are in very good agreement with the experimental
observations.
Consider the scattering of an α particle by a thin metal foil. Let the cross
sectional area of the beam be A. Then the total number of atoms which scatter
the α particles is
n = ρ At
(2.50)
where ρ is the number of atoms per unit volume, and t is the thickness of the
foil. For each atom, let the incoming α particles in the impact parameter range