ATOM MODELS, QUANTUM NUMBERS, PAULI EXCLUSION PRINCIPLE. 2. előadás

Transcription

1 ATOM MODELS, QUANTUM NUMBERS, PAULI EXCLUSION PRINCIPLE 2. előadás

2 Plum pudding model of atom Thomson atom model

3 Rutherford atom model University of Manchester 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

4 Rutherford atom model Alpha-particles Gold atoms Explaining: 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

5 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.

6 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.

7 II. Atom model from Bohr Bohr model If the electron moves from one energy level to another one, the energy of it radiates or emitts as: W n W k = h f Energy of photon is equal to the difference of the energy levels.

8 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.

9 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: L = l h 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

10 Magnetic quantum number z Bohr-magneton: M B = e h 2m e 2π L M z M e v Angular momentum of an atom: M = M B l Perpendicular projection of the angular momentum vector to the axis of Z: M z = M cosα = M B l cosα Definition: (magnetic quantum number): m = l cos α m = 0, ±1, ±2, m = l, 0,, +l

11 Definition (spin): Spin The quantity of L S = ± 1, where h is 2 2π the Planck-constant is called as spin. (not equal as spin quantum number!!) Definition (spin quantum number): The value of ± 1 = s in the definition 2 formula of spin we call as spin quantum number. h

12 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.