RUTHERFORD'S EXPERIMENT
In the year 1898
Thomson created the idea of atom
as the positive charged ball in which there are negative charges
placed - the "plum cake"
model. So summing up the whole atom were to be neutral.
In the years
1909-1911 Ernest
Ruthefordand his students - Hans Geiger (1882-1945) and Ernest
Marsden conducted some experiments to search the problem of alpha
particles scattering by the thin gold-leaf. Rutheford knew that the
particles contain the 2e charge. The experiment caused the creation
of the new model of atom - the "planetary"
model.
Rutheford suggested to hit the gold-leaf (picture
no. 1) with fast alpha particles from the source 214Po.
(The source R was in the lead lining F). The particles felt from
the source on the gold-leaf E and were observed by the microscope
M. The whole experiment was in the metal lining A and was covered
with the glass plate P. The instrument was attached to the footing
B. The gold leaf was about 5*10-7 meter thick. The
scientist knew that reckoning the scattering angle could say much
about the structure of atoms of the gold-leaf.
Rutheford made a theoretical analysis of angles of
scattering in accordance with Thomson's theory of atom and in
accordance with his own theory. He assumed that atom consisted of
positive charged nucleus and negative charged electrons circling
around the nucleus. Then his theoretic calculations he compared
with the experiment result. Alpha particles going through atom
created in accordance with the
"plum cake" model wouldn't be strong abberated because the
electric field in that atom wouldn't be strong. In the model
created by Rutheford the field
is much stronger near to the nucleus, so some of alpha particles
are much more abberated. The other going in the far distance to the
nucleus are almost not at all abberated. The probability that any
alpha particle will hit the nucleus is small but there is such a
chance.
The experiment showed
that there are some not much abberated alpha particles but also
some abberated of a very big angle (135-150 degree). That
occurrence couldn't be explained by some small, added aberrations.
Experimental data proved the "planetary" model of atom.
Between an alpha
particle and an atomic nucleus there subsist an interaction - the
repulsing - according to Coulomb
force:
(1)
where (2*e)- alpha particle charged, (Ze)- atomic nucleus charged,
y0 - permittivity of free space, r - distance between
the nucleus and the particle. Then, according to the formula
created by Rutherford> (we
decided not to present the run of this thoughts leading to the
formula because it's very complicated from the mathematical side),
dN - the number of alpha particles scattered in a time unit inside
the solid angle dQ is equal:
(2)
where n - alpha particle flux density, G - angle of scattering
alpha (picture no. 2), E particles' energy.
On the base of the
number of alpha particles scattered by the G angle the Z number of
elementary, positive charges in the nucleus can be calculated. He
found that the number is equal to the atomic number. If we know the
charge of the nucleus we can calculate the upper limit of its
radius (by the assumption that the nucleus is a ball). The of the
alpha particles and the nucleus radius is smaller than the minimum
limit r0 between their centres in the moment of
collision. To evaluate r0 lets consider the central
collision - scattering by the angle G = 180 degree. By the law of
conservation of energy - in the moment, when the distance between
the alpha particles and the nucleus is minimal, the kinetic energy
of that alpha particle is completely changed to the energy of the
interaction:
(3)
where m - alpha particle mass, v - alpha particle velocity before
the collision.
After transformation:
(4)
From the equation (4)
for the gold of this experiment the r0 value was about
3,1*10-14 meter (the velocity of alpha particles was
equal 1,9*107 meter per second). Nucleus dimension have
to be smaller than that quantity.
Summarising the results
of his work Rutherford came to
the opinion that atom consisted of a nucleus (of size
10-15 to 10-14 meter). The nucleus contains
the whole positive charge and almost the whole atom's mass. Around
the nucleus, on the area of the size of the order of
10-10 meter, light electrons are circling. Electrons
have to circle around the nucleus on orbits, not to fell down on
the nucleus. The orbits depend on electrons energy. In atoms of the
same element, electrons circle on the same characteristic, for that
element, orbits - the optical spectrum of atoms of the same element
is the same.
The model created by
Rutherford had still some
serious discordance. According to the classic science, electron
moving around the nucleus should emit an electromagnetic wave. That
kind of emission is connected with the escape of some energy from
the electron-ion circuit. Electron should than move not by the
circle but helical and finally collide with the nucleus. But atom
is stable. Other discordance regarded the radiation - it were to be
constant (because the time of electron's cycle in accordance with
the lost of energy should change constantly) and spectral lines
shouldn't occur.
The model of atom
created by Rutherford couldn't
be the conclusive model of matter's constitution.
- Computer programm -
experiment simulation
