Atomic models
Thomson’s model (1865-1940)
Rutherford’s model
Bohr’s model
Atomic model origins
The word atom comes from the greek word atomos which means
indivisible
The atomic vision of nature was created by the mind of the greek
philosopher Democritus, who, beliving impossible that bodies could be
divided indefinitely, postulated the existence of final particles not longer
divisible, just called atoms.
The hypothesis of the existence of microscopic particles has been
repeatedly taken into account during the history of physics, but their
existence, until the early years of the twentieth century, was not yet proven
with certainty and was challenged by many.
The emission spectra of atoms
Many experiments carried out at the end of the 19th century were passing
very intense electrical discharges through the gases and analyze later the
light that these gases emitted.
The light emitted under these conditions, analyzed with a spectroscope,
emphasize the lines of the emission spectrum of the gas.
Changing the type of gas the type of spectrum changes, both in number of
rows, in both their spacing, in both their intensity
Thomson’s model (1904)
Plum Pudding Model
The atom was constituted by a distribution
of positive charge within which the
negatives charges are present. The atom is
electrically neutral.
NB JJ Thomson, English physicist and director of one of the most famous
research centers in the time, the Cavendish Laboratory in Cambridge,
discovered the electron in 1897.
Other features of the model of Thomson:
The electrons revolved within the positive charge.
The orbits described were made stable by the interaction between
positive and negative charges.
The differences in the spectra of emission of the various substances
were traced to differences of energies of the different electron
orbits.
The model was not confirmed by the experimental data on the
atomic spectra of the main elements (anyone couldn't find a stable
configuration of the atoms providing for the emission spectra
observed ).
Rutherford’s experiment
In 1909 the physicists Geiger and Mardsen, under the
direction of Rutherford, make an experiment to confirm
Thomson's model.
They shoot a gold leaf with alpha particles ( got from
radioactive decline of radium).
A sheet of zinc sulphide surrounding the gold leaf served as
a detector (the zinc sulphide outputs sparks when it was hit
by alpha particles).
Rutherford’s experiment:
aims
Measuring the alfa particles' deflection, physicists could get
informations on the distribution of charges in the atom.
According to Thomson's model, the alfa particles had to
cross the gold leaf undergoing little deflections (of few
degrees).
Rutherford’s experiment:
results
Obtained results were clearly in conflict with Thomson’s
model hypothesis:
Some alfa particles (about 1/8000) were deflected with
angles bigger than 90°
“It was quite the most incredible event that has ever happened to me
in my life. It was almost as incredible as if you fired a 15-inch shell at
a piece of tissue paper and it came back and hit you. On
consideration, I realized that this scattering backward must be the
result of a single collision, and when I made calculations I saw that it
was impossible to get anything of that order of magnitude unless you
took a system in which the greater part of the mass of the atom was
concentrated in a minute nucleus. It was then that I had the idea of
an atom with a minute massive centre, carrying a charge.”
Fu l'evento più incredibile mai successomi in vita mia. Era quasi
incredibile quanto lo sarebbe stato sparare un proiettile da 15
pollici a un foglio di carta velina e vederlo tornare indietro e
colpirti. Pensandoci, ho capito che questa diffusione all'indietro
doveva essere il risultato di una sola collisione e quando feci il
calcolo vidi che era impossibile ottenere qualcosa di quell'ordine di
grandezza a meno di considerare un sistema nel quale la maggior
parte della massa dell'atomo fosse concentrata in un nucleo molto
piccolo. Fu allora che ebbi l'idea di un atomo con un piccolissimo
centro massiccio e carico.
Rutherford’s experiment:
results’ interpretation (1911)
In an article published in 1911 Rutherford refuted Thomson’s
model and proposed a model in which thepositive charge was
concentrated in a space smaller than atomic sizes (atomic nucleus)
and was responsible of alfaparticles’ deflection.
Electrons, negatively charged, revolved around the nucleus for the
Coulomb effect of attraction
He could define the gold atom nucleus’ radius (3.4 x 10−14 m) and
the gold atomic radius (1.5 x 10−10 m)
Bohr’s atomic model
Bohr noticed a contradiction in Rutherford’s planetary model: a
charged particle that rotates (the electron) moves with centripetal
acceleration and therefore must radiate energy (of the same
frequency of its motion).
The continuous electromagnetic radiation should produce a
consequent loss of kinetic energy by the particles which then
should fall on the nucleus with a trajectory similar to a spiral.
Bohr calculated that the electron would take a time of 10/8 s to fall
on the nucleus. then the Rutherford atom was not stable.
The quantization of the energy
of the atom
To solve the problem of stability of the atom; Bohr postulated the existence
of discrete energy levels, levels quantized that match to stationary states of
the whole atom, in which the motion of rotation of the electrons were not
changed by the passage of time.
In Bohr's model the sequence of atomic energy levels starting from the
ground state of the atom, corresponding to the lower energy.
Other levels correspond to excited states of the atom, and electrons in them
have higher energy than the ground state.
Going from an excited state to the fundamental one, electrons give
excess energy in the form of radiation.
Bohr’s postulates
In 1913, Bohr published his hypothesis on the quantized nature of atomic
energy, formulating the following postulates:
1. Electrons can rotate stably without radiate only on certain orbits called
stationary states. The irradiation of the atom takes place when one or
more electrons pass from one stationary state to another.
2. The frequency (f) of the emitted radiation does not coincide with the
frequency of rotation of the electron in any orbit, but matches to the
one that is obtained by the relation of Plank
E  E  hf
f
i
E f , Ei
where
are the energies corresponding to the final and the
initial state and h is Plank's constant
h  6,626 1034 J  s
The second postulate takes the special meaning of the principle of
conservation of energy through the emission or absorption of a photon in
the appropriate electron transitions.
Infact
it implies that if an electron moves from one energy state upper (outer orbit)
to a lower one (innermost orbit), the lost energy is emitted as a photon ( the
"quantum" of light assumed by Einstein) of frequency.
Vice versa
the absorption, by the atom, of a photon with energy hf exactly equal to the
difference between two stationary states, causes the transition of the
electron from a lower energy level to a higher one.
Hydrogen atom in Bohr's model
L’atomo di idrogeno è composto da un elettrone di massa me
e carica –e che ruota su una circonferenza di raggio r attorno ad un
protone di carica +e .
La forza responsabile della rotazione è la forza coulombiana
F
(e)( e)
40
r2
1
Tale forza si comporta come una forza centripeta, quindi:
me
v2
1 (e)( e)

r 40
r2
da cui si ottiene
v2 
1 (e)( e) r
1
e2


40
r2
me 40 me r
e un’energia cinetica dell’elettrone
K
1
1
1
e2
1 e2
me v 2  me

2
2 40 me r 80 r
Hydrogen atom in Bohr's model
L’energia potenziale (elettrica) dell’elettrone è data dalla formula
U
1 (e)( e)
1 e2

40
r
40 r
The total energy of the electron may be obtained by summing the kinetic
and the potential energy.
Etot  K  U 
1 e2
1 e2
1 e2


80 r 40 r
80 r
Bohr’s atom radius r, velocity v of the electron and its total energy can not
take any values but only a set of values determined.
Quantization conditions
Secondo Bohr la condizione di quantizzazione che permette di stabilire
quali sono le orbite permesse nel caso dell’atomo di idrogeno è la seguente:
2rn pn  nh
Dove h è la costante di Planck
h  6,626 1034 J  s
n è un numero intero positivo detto numero quantico principale
rn
è il raggio dell’orbita numero n
pn è la quantità di moto dell’elettrone su questa orbita (massa per
velocità)
Quantization conditions
La condizione di quantizzazione
2rn pn  nh
può essere scritta nella forma
2rn me vn  nh
ed elevando al quadrato
4 2 rn2 me2 vn2  n 2 h 2
2
e
Sostituendo l’espressione per la velocità v 
40 me r
2
n
si ottiene
e2
4 r m
 n2h2
40 me rn
2 2
n
2
e
1
ovvero
rn me
1 e2
0
 0h2
2
 n h  rn  n

n
a0
2
me e
2
2
2
1
Quantization conditions (radii)
Bohr dimostrò quindi che i raggi delle orbite stazionarie dell’elettrone
dell’atomo di idrogeno sono quantizzati secondo la legge


rn  n 2 a0  5,29 10 11 m  n 2
Per un atomo di numero atomico Z la relazione precedente diventa
rn  n 2
a0
Z
I raggi delle orbite permesse sono dunque direttamente proporzionali
al quadrato del numero quantico principale
Quantization conditions (energy)
Sostituendo la relazione trovata
 0h2
2
rn  n

n
a0
2
me e
2
nell’espressione dell’energia totale
1 e2
Etot  
80 r
si ottiene
me e 4 n 2 1
e 2 me e 2
13,6eV
Etot  




2
2
80  0 h 2 n 2
n2
8 0 h 2 n
Questo vuol dire che per poter estrarre un elettrone nello stato fondamentale
dell’idrogeno (n=1) bisogna fornire al sistema un’energia pari a 13,6 eV .
Inoltre le energie permesse sono dunque inversamente proporzionali al quadrato
del numero quantico principale
1eV  1,6 1019 J
The spectrum of hydrogen atom
According to Bohr's hypothesis, an electron emits (receives) a photon when it moves
from one allowed orbit of greater energy (smaller) to one allowed orbit of lower
energy (higher).
NB the total energy of the electron is negative and inversely proportional to r. The
orbits of greater energy are the orbits more external.
When the atom is energized, it receives energy from the outside (for example when the
gas is crossed by current) and the electron moves to the greater energy orbit than
initial, such as E(n).
Under these conditions the electron, after a very short interval, jump on a lower energy
orbit E(m) with m<n.
The difference of energy is released as photon of frequency
E E (n)  E (m)
me4  1
1
f  
 2 3 2  2
h
h
8 0 h  m n 
The spectrum of hydrogen atom
The previous formula
me4  1
1
f  2 3 2  2
8 0 h  m n 
Is the same as the physicist Balmer found empirically in 1885, concerning the
frequencies of visible lines in the spectrum of the hydrogen atom.
1 
 1
f  cRH  2  2 
n 
m
Dove c è la velocità della luce, n è un intero maggiore di 2 e
è una costante di proporzionalità
R  1,097 107 m1
H
Then Bohr’s model is in agreement with the experimental data.