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THE QUANTUM MODEL OF THE ATOM QUANTUM MECHANIC MODEL • Louis de Broglie • Werner Heisenberg • Erwin Schrodinger ELECTRONS AS WAVES • Louis de Broglie • 1924 • Suggested that electrons be considered waves confined to the space around an atomic nucleus • Electron waves could only exist at specific frequencies that correspond to specific energies THE HEISENBERG UNCERTAINTY PRINCIPLE • Werner Heisenberg • 1927 – German theoretical physicist • Idea involved the detection of electrons, which are detected by their interactions with photons • Because photons have about the same energy as electrons, any attempt to locate a specific electron with a photon knocks the electron off its course • Results in uncertainty in trying to locate an electron or any other particle • Heisenberg uncertainty principle: states that it is impossible to know both the position and velocity of an electron or any other particle at a given time THE SCHRODINGER WAVE EQUATION • Erwin Schrodinger • 1926 – Austrian physicist • Developed an equation that treated electron in atoms as waves • Schrodinger equation (+ the Heisenberg uncertainty principle) laid the foundation for modern quantum theory • Quantum theory: describes mathematically the wave properties of electrons and other small particles • Solution to Schrodinger equation is known as a wave function • Only gives the probability of finding an electron at a given place around the nucleus • Electrons do not travel in neat orbitals • Orbital: 3-dimensional region around the nucleus that indicated the probable location of an electron ATOMIC ORBITALS AND QUANTUM NUMBERS • Quantum numbers: specify the properties of atomic orbitals and the properties of electrons in orbitals • Four quantum numbers: • 1. Principal quantum number • 2. Angular momentum quantum number • 3. Magnetic quantum number • 4. Spin quantum number • Principal quantum number (n): indicates the main energy level occupied by an electron • Only positive integers n= 1, 2, 3, 4… • As n increases, the electron’s energy and average distance from the nucleus increases • Each main energy level has sub-levels • Maximum number of electrons in a principal energy level is n2 • Angular momentum quantum number (l): indicates the shape of the orbital • For a specific main energy level, the number of orbital shapes possible is equal to n • Values of l allowed are 0 and all positive integers less than or equal to n-1 • n=1 has one sublevel (s) • n=2 has two sublevels (s and p) • n=3 has three sublevels (s, p, and d) • n=4 has four sublevels (s, p, d, and f) Orbital Letter Designations According to Values of l Principal (n) Angular momentu m (l) Letter 1 0 s 2 1 p 3 2 d 4 3 f S ORBITAL P ORBITAL D ORBITAL F ORBITALS • Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel • Examples: • 1s = the s orbital in the first main energy level • 1p = the p orbital in the first main energy level • 2p = the p orbital in the second main energy level • 4d = the d orbital in the fourth main energy level • Magnetic quantum number (m): indicates the orientation of an orbital around the nucleus • Describes the orientations that correspond to various values of m m= -l to +l • One s orbital in each s sublevel • Three p orbitals in each p sublevel • m=-1, m=0, m=+1 • Five d orbitals in each d sublevel • m=-2, m=-1, m=0, m=+1, m=+2 • Seven f orbitals in each f sublevel • m=-3,m=-2, m=-1, m=0, m=+1, m=+2, m=+3 • Spin quantum number: indicates the two fundamental spin states of an electron in an orbital • Only two possible values: - ½ and + ½ A single orbital can hold a maximum of two electrons, which must have opposite spins