Download Limits of classical physics II.

ATOM MODELS,
QUANTUM NUMBERS,
PAULI EXCLUSION PRINCIPLE
2. előadás
Plum pudding model of atom –
Thomson atom model
Rutherford atom model
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University of Manchester
1909 – 1911
Hans Geiger, Ernest Marsden
Ernest Rutherford lead the team
Experiments in order to map the structure of gold atom
Gold foil was bombed by alpha-particles
Waited for:
alpha particles will slow down in the atom foil, but they will keep they original direction of
motion.
Results observed:
some alpha particles refracted or reflected back from the target
alpha particles scattered or back-scattered on the gold target
Rutherford atom model
• Explaining:
Alpha-particles
Gold atoms
– Structure of the gold atoms can
not be described by the plum
pudding model
– If the plum pudding model would
be valid, the alpha particles would
keep their original moving
directions
– Alpha particles scattered on gold
atoms 
– Local, relative heavy, positively
charged spreading centers should
be located inside gold atoms
– Atom has core.
– Core of the atom is heavy (mass of
the atom is centered to the core)
– Core of the atom is positively
charged
Rutherford atom model
Atom model of Rutherford:
Core of atom exists.
Mass of the atom is centered into the core of the atom.
Core of the atom has positive discharge.
Electrons make circular motion around the core of atom due to the centripetal force
originating from the core.
Something is wrong with the atom model of Rutherford:
If the electron moves on a circle (circle motion with constant speed) 
Electrons should move as an accelerating particle  accelerating particle should radiate in
the ground state as well  Electrons should lose their energy  Radius of the circle of
circular motion should decrease continously  Electrons should travel to the core 
Electrons should fell into the core.
But: electrons in the ground state do not radiate!!! Electrons do not fell into the core.
The theory from Rutherford can not be valid.
Atom model from Bohr – Bohr model
I.
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts
the atom as small, positively charged nucleus surrounded by electrons that
travel in circular orbits around the nucleus—similar in structure to the solar
system, but with attraction provided by electrostatic forces rather
than gravity. After the plum-pudding model (1904), and the Rutherford
model (1911) came the Rutherford–Bohr model or just Bohr model for short
(1913). The improvement to the Rutherford model is mostly a quantum
physical interpretation of it. The Bohr model has been superseded, but the
quantum theory remains sound.
Atom model from Bohr – Bohr model
II.
If the electron moves from one energy level to another one, the
energy of it radiates or emitts as:
𝑾𝒏 − 𝑾𝒌 = 𝒉 ∙ 𝒇
Energy of photon is equal to the difference of the energy levels.
Atom model from Bohr – Bohr model
Angular momentum of the electron:
Paths of the electrons in the atom are defined by the
angular momentum,
according to the formula given above.
Definition (Principal quantum number):
The letter of „n” (n is a positive integer) in the formula given above is called as
principal quantum number.
Bohr-Sommerfeld atom model
• Spectral line structures of an atom show fine structure.
Fine structure: a spactral line holds more very thin lines.
• Sommerfeld corrected the Bohr-model:
𝒉
𝑳=𝒍∙
𝟐𝝅
• Sommerfeld introduced ellyptical trajectories around the
circular main electron trajectories.
• Definition (azimuthal quantum number):
The letter of „𝑙” belong to the angular momentums of an
atom is called as azimuthal quantum number. It connects to
the ellyptical paths of the electrons.
𝒍 = 𝟎, 𝟏, 𝟐, 𝟑, … 𝒏 − 𝟏, where 𝒏 is the principal quantum
number
Magnetic quantum number
z
Bohr-magneton: 𝑴𝑩 =
𝒆
𝟐𝒎𝒆
∙
𝒉
𝟐𝝅
Angular momentum of an atom:
𝑴𝒛

𝑴
𝑴 = 𝑴𝑩 ∙ 𝒍
Perpendicular projection of the angular momentum vector
to the axis of Z:
𝑳
𝑒−
𝒗
𝑴𝒛 = 𝑴 ∙ 𝒄𝒐𝒔𝜶 = 𝑴𝑩 ∙ 𝒍 ∙ 𝒄𝒐𝒔𝜶
Definition: (magnetic quantum number):
𝑚 = 𝑙 ∙ cos 𝛼
𝒎 = 𝟎, ±𝟏, ±𝟐, … 𝒎 = −𝒍, … 𝟎, … , +𝒍
Spin
• Definition (spin):
𝟏 𝒉
±
,
𝟐 𝟐𝝅
The quantity of 𝑳𝑺 =
where h is
the Planck-constant is called as spin.
(not equal as spin quantum number!!)
• Definition (spin quantum number):
𝟏
The value of ± = 𝒔 in the definition
𝟐
formula of spin we call as spin quantum
number.
Pauli exclusion principle
Pauli exclusion principle:
The Pauli exclusion principle is the quantum
mechanical principle that no
two identical fermions (particles with halfinteger spin like electrons) may occupy the
same quantum state simultaneously.
Comment:
Pauli exclusion principle helps us to
understand the structure of the periodic table
of elements.