In 1905 Albert Einstein extended to all the physical phenomena the relativity
principle, that was formulated by Galileo for the mechanical phenomena and concerns the
equivalence of all the inertial frames of reference, that is the not accelerate ones, as
regards the acceleration of a body subiected to forces.
Einstein, after have assumed
the invariability of the modulus of the velocity of light in any frame of reference, besides the
(Lorentz's) transformation relations for spatial coordinates, necessary to describe a physical
phenomenon in the transit from a inertial frame of reference to another, he considered the
transformation of time, by introducing the concept of local time, that is the time
measured by an observer in his own frame of reference, and by treating the time as the fourth
co-ordinate in space-time.
From time relativization, that is a direct
consequence of the finite and constant value of the velocity of light, derives the
difference of the local duration of a physical phenomenon that is developing in an
inertial frame of reference, in comparison with that appraised by another observer in an
inertial frame of reference which is in rectilinear and uniform motion with respect to the first one.
As concerns dynamics, Einstein introduced the rest mass (mo), measured in a frame of reference in which a body is at rest, and the relativistic (or motion) mass m (v), that depends from the velocity (v) of the body referred to a generic inertial frame, in which it is in motion.
The relativistic mass depends on the velocity according to a law saying that a body with a non-zero rest mass, to be moving with the velocity of light, it needs an
infinite kinetic energy.
In fact, because the mass is increasing with the velocity, it
becomes infinite when the velocity is near to the value of the velocity of light, and
therefore it is requested an infinite kinetic energy for v = c =
300000 Km/s.
The mass increase of a body is meaningful only when the velocity becomes
comparable with the one of light.
Therefore, the field of the ideal verification of the m(v) law , is the one of subatomic particles, whose velocity is very
near to the one of light.
Another ,very important consequence of relativistic
effects, is the mass-energy conservation law, which implies the classical principles of
the mass conservation and the one of energy conservation are unified in an only law, the
so called mass-energy conservation law.
This law says that the variation of mass of a
body, for an amount Dm = m-mo, is always associated to an emission or to an absorption of the energy
DE = Dm c2.
This law allows to explain the operation of nuclear reactors, the origin and evolution of stars and all the
interactions among elementary particles in high-energy physics experiments .
The photoelectric effect consists in emission of electrons by a metallic surface on
which is exposed to a light flux.
The effect takes place easily using metals as cesium,
whose conduction electrons is weakly tied to ions of crystal lattice, in such a mode
that it is needful a modest quantity of energy (extraction work) to extract them from
a metal.
It is observed that every metal is characterized from a threshold wavelength,
over which the photoelectric effect doesn't take place, and that the maximum speed of
photoelectrons doesn't depend on the illumination intensity of the metallic surface.
It is also observed that the intensity of the photoelectric current is directly
proportional to the illumination intensity.
By the laws of classical physics it isn't
possible to explain the characteristics of this phenomenon.
It is owing to Albert Einstein
( Nobel prize winner in 1921 ) the theory of the photoelectric effect, that is based on
the hypothesis of photons.
In fact Einstein, assuming as a postulate the quantization of
energy, introduced by Max Planck in the study of the thermal radiation emitted by the black
body (an ideal body characterized from the maximum emitting and absorbing power of the thermal radiation
),
did the hypothesis that photoelectrons are extracted from the metal as a consequence of
their collisions with electromagnetic energy packets E = hf =
hc/l, the so-called photons or quanta of light, where h is Planck's constant,l is the wavelength and f is the frequency of the electromagnetic radiation absorbed by the metal.
In such a mode, the maximal kinetic energy
K with which are emitted photoelectrons, is given by the
difference between the energy E of the colliding photon and the
extraction work W ,which is characteristic of each metal:
K = E - W.
It is immediate to understand the existence of a
threshold wavelength, if we thinks that extracting an electron needs a photon with an energy at least
equal to E = hc/lo - W, where lois the threshold-wavelength.
The fact that the intensity of the photoelectric current is proportional to the illumination intensity, is explained easily by thinking that exists a 1:1 ratio between the number of emitted photoelectrons and the one of absorbed
photons, and that a ray of light is much more intense, the greater is the number of
photons associated to it.
The validity of photon hypothesis was confirmed
experimentally after the discovery of Compton effect (1923) , consisting in scattering of X and g photons by a light weight atoms against which they collide,
with a variation of photon energy.
It was observed for the first time
in a cloud chamber (a Wilson chamber ) the scattering of photons by electrons
weakly-tied to nucleus, with increasing of the wavelenght of scattered radiation with respect to the one of incident radiation.
The consequent energy diminution of photons is equal to the kinetic energy of the electrons scattered by collision with photons.
The existence of photons is a consequence of the wave-particle-like dualism observed for electromagnetic radiation: electromagnetic radiation behaves as an electromagnetic wave beam, when it is travelling in a region with spatial dimensions much
great in comparison with the ones of atoms.
When instead are considered atomic phenomena ,
electromagnetic radiation behaves as a beam of particles,that is energy packets, that is photons,which
move with the velocity of light and interact with subatomic particles according to the energy and momentum conservation laws.
The English physicist Rutherford, helped by Geiger and Marsden, by means of several famous experiences effected at Cambridge University and consisting in bombarding thin gold layers with a particles (helium nuclei), discovered that nearly the whole mass of an atom is
concentrated in its nucleus, having a positive electric charge and surrounded by electrons orbiting around it.
After discovery of X-rays and their wave-like nature,evidenced because they are
deflected neither by electric nor magnetic fields, their wavelength had to be measured.
In
1913 the German physicist Max Von Laue ( Nobel prize winner in 1914 ) and the English
physicists William Bragg and William Lawrence Bragg, father and son, (Nobel prize winners
in 1915), by using crystals of vary types succeeded in getting some photographic images of the
diffraction figures that were generated by interposing a crystal on the trajectory of X-rays.
W.H. Bragg and W.L. Bragg succeeded besides in measuring the wavelength and, after having
improved the measure method of it by their invention of X-ray spectrometer,
they were able to measure interatomic distances of many crystals, starting
the X-ray diffractometry, which has a fundamental importance in studying the structure of
matter.
Within the second decade of the twentieth century the physicists Rutherford, Bohr and
Sommerfeld, developing Planck and Einstein's quantum theories about, respectively, the quantization of the electromagnetic radiation energy emitted by the black body, and the one of the electromagnetic energy absorbed by a metal emitting electrons by the photoelectric effect, they conceived the first quantum theory useful to calculate the wavelength of the optical and X-ray line spectra of hydrogen atom and of other one-electron atoms, that is helium and ionized lithium .
In particular the Danish physicist Bohr ( founder of the physics school at Copenaghen University and Nobel prize winner in 1922 ) , starting from the Rutherford's discovery of the atomic nucleous, proposed the first atomic model.
According to Bohr-Rutherford's model one atom is seen as a solar microscopic system to whicj can applied the laws of classical physics and some postulates to take account that, in the atomic micro-world, energy and angular momentum are quantized and that therefore their values are always multiples of an elementary quantity of energy
( E = h f ) or angular momentum L = nh/(2p) ,
where f is the frequency of the electromagnetic radiation,h is the universal Planck's constant and n is an integer number.
Bohr-Rutherford's model, improved by Sommerfeld by considering some relativistic effects, although is much elementary from a mathematical point of view, however it allows to calculate the energetic levels of one-electron atoms, but not the probability of transition of an
electron between two energy levels, which is fundamental to calculate the relative
intensity of the spectroscopic lines emitted or absorbed by atoms .
The French physicist De Broglie (Nobel prize winner in 1929), extending to matter the
wave-particle-like dualism introduced by Einstein's hypothesis of photons, proposed
to associate with a particle with mass M , that is moving
with velocity V, the wavelength
l = h /(MV),
where h is Planck's constant.
This hypothesis allows to attribute
to every material particle a wave-like nature,that is the more significant, the smaller is the particle
momentum p = MV.
Therefore the wave-like effects results
negligible if the mass of a particle is much greater of the one of micro-world particles forming atoms.
The elementary atomic model of Bohr-Rutherford represented only a provisional
theoretical approach in waiting for an atomic complete theory .
The German physicist Erwin
Schroedinger (Nobel prize winner 1933 ), assuming as a starting point the wave-like
hypothesis of matter, built a quantum theory of the atom based on an equation suitable to
describe the wave-like behaviour of atomic electrons.
Schroedinger's equation, originally
conceived to describe the material waves associate to electrons, was reinterpretataed
by Max Born ( Nobel prize winner 1954 ) as the probability-wave equation.
Therefore the
Schroedinger equation ,when it is applied to an electron microsystem with one, two or many
electrons (a atom,a molecule or a crystal ), admits as a solution the so-called wave function, a
function of the spatial coordinates, from which can be calculated the density of
probability to find an electron in a generic point of space around nucleous.
Schroedinger's
equation admits physically acceptable solutions (eigenfunctions) only for some particular values of energy,
the so-called eigenvalues, that coincide, for example in the case of
hydrogen atom, with the energetic levels of its only electron.
Likewise, by applying
the wave equation to a molecule or to a crystal, it is gotten a wave function
(eigenfunction), from which can be calculated the molecular electronic density or the crystalline one.
The quantum mechanics of Schroedinger, said even wave-mechanics, is a complete theory, as it permits to calculate both the energy levels of the electrons in atoms, molecules and
crystals, and the probability of transition between two quantum states.
The wave equation
can be applied to any elementary particle that is moving in a force field, in particular,
around an atomic nucleus, to calculate the energy levels of nucleons, protons and neutrons
subjected to the potential energy of the nuclear forces.
The German physicist Werner Heisenberg (Nobel prize winner 1932 ), independently from
Schroedinger's work, formulated the quantum mechanics assuming as a fundamental its
uncertainty principle and elaborating a mathematical approach based on the matrixes
(the matrix quantum mechanics).
Every observable physical quantity , that is energy,
position, momentum, angular momentum , is described by an operator represented as a matrix,
with results that are formally analogous to the ones of Schroedinger'equation.
The uncertainty
principle, that in the matrix mechanics functions as the wave-like De Broglie
hypothesis in Schroedinger's quantum mechanics, affirms that the uncertainties (errors)
associated with the simultaneous measure of two complementary physical quantities (position and
momentum or energy and time ), are each other inversely proportional:
Dx .
Dpx ~= h/(2p) ;
DE .
Dt ~= h/(2
p),where h is the Planck constant.
In other words, if by an
experiment one determines, for example, the momentum of a particle, with a very small
error Dpx , the corresponding
error Dx made in the simultaneous
measure of the co-ordinate x of the particle is much great,
and it is inversely proportional to Dpx.
In 1922 the German physicists Stern (Nobel prize winner 1943 ) and Gerlach, while
studying the effect of a non-uniform magnetic field on silver atoms, to verify the
quantization of the atomic magnetic moment associated with the angular momentum of
electrons, they discovered that a well collimated beam of non-ionized Ag atoms, crossing
the space between the polar expansions of a magnet, that is shaped in such a mode to get a
non-uniform field, to apply to atomic magnetic moments a force instead a
torque, is divided in two beams, in such a mode that isn,t foreseen by classical physics,
according to which the beam should spread in many elementary beams distributed with
continuity in a certain angle, nor by quantum theory, according to which it
should spread to form some beams oriented in a discreet number of directions.
The
experiment was repeated in 1927 from Phipps and Taylor with non-ionized hydrogen atoms and
without a magnetic moment, as they were in the ground state , that is with the least
energy and the angular momentum equal to zero, and it was observed even in such conditions the
dual splitting of the beam, that couldn't be determined by the magnetic moment associated
with the orbital angular moment of the electrons, because it was equal to zero.
The
experiment was explained by admitting the existence of an associate magnetic moment to an
intrinsic angular momentum of electron, not foreseen by the classical physics nor from
the non-relativistic quantum mechanics of Schroedinger.
The intrinsic angular momentum of
an electron may be seen as a microscopic spinning top, that takes the name of "spin" .
Electron spin and the one of other particles ( protons, neutrons,etc...
) is a moment of intrinsic
rotation which is typical of quantum mechanics and whose existence is able to be justified only within a relativistic quantum theory, as the one elaborated by the English physicist P.A.M. Dirac in 1928.
The physicists Clinton Davisson and George Thomson (Nobel prize winners in 1937 ),
experimenting electron scattering by nickel crystals, were able to get some diffraction figures
analogous to that gotten by Laue with X-rays, and got so the first experimental evidence
of the validity of the De Broglie wave-like hypothesis .
In some following experiments,
performed from other physicists with gold layers and crystals of several types, were gotten
some photographic imagines of diffraction rings quite similar to that gotten by using
X-rays.
The experiments of Davisson and Thomson confirmed the existence of the
wave-particle-like dualism of the matter, besides the one observed for electromagnetic radiation.
Therefore, besides the X-ray diffractometry there is the electron diffractometry, that has today a
fundamental importance in the researches on the structure of the matter, that is based on
measures of the electronic density in crystals.
We remember that the ion and electron
microscopes use the wave-like properties of ions and electrons respectively, to produce diffraction
images of biological tissues and various materials.
The quantum mechanics ( wavemechanichs ) based on Schroedinger's equation
doesn't take account of Einstein's theory of the special relativity, and therefore it
cannot explain all the properties of the elementary particles that constitute the matter,
when the velocities that are considered, are not negligible in comparison with the ones of
light.
For example, any characteristics of the optical and X-ray line-spectra emitted by
atoms cannot be explained within the Schroedinger theory , that don't take account of
Einstein's space-time and of the transformation rules of the space-time coordinates in the
transit from a inertial frame of reference to another one that is moving in comparison with the
first with a rectilinear and uniform motion.
A relativistic formulation of quantum mechanics
was developed by the English physicist Paul Adrien Maurice Dirac (Nobel prize winner in
1933 ), that wrote a relativistic wave equation that is invariant with respect to the
relativistic transformations of the space-time co-ordinates.
The fundamental
characteristics of the equation introduced by Dirac consisted in including naturally the
spin of the particles, as a direct consequence of the relativistic formalism, and in
assigning to a particle two possible values of energy, different only for the sign.
The
interpretation proposed by Dirac for the states with a negative energy associated to an
elementary particle, it is based on the hypothesis of the existence of the relative
antiparticle, that is of an antiparticle having a mass equal to the one of the particle and an
electric charge of opposite polarity.
The first experimental evidence of the existence of a
particle-antiparticle pair was obtained in the years 1932-33, when Anderson ( Nobel prize
winner in 1936 ), Blackett ( Nobel prize winner in 1948 ) and Occhialini, while studying
the showers of the secondary particles produced by the cosmic rays in the earth
atmosphere, discovered the antiparticle of the electron, the positron or positive
electron.
. Some years after ( 1955 ), the Italian physicist Emilio Segrč (Nobel
prize winner in 1959), while concluding a series of experiments effected with the cyclotron
by 6,2 GeV of the Berkeley University, succeeded in producing antiproton, furnishing a
further, bright confirmation of the validity of Dirac's relativistic quantum mechanics.
