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MODERN QUANTUM THEORY Werner Heisenberg German physicist 1901 – 1976 Leader in the development of quantum theory in the 1920’s Heisenberg carried out a careful analysis, which showed that it is not possible to determine as electron’s momentum (mass x volume) and its position/location simultaneously. IF we know one we cannot know the other. This is known as the Heisenberg’s uncertainty principle: it is impossible to determine the location and momentum of an electron simultaneously. But electrons can be described as being located in orbitals, which are 3d spaces where there is a high probability of an electron being found. The size, shape and orientation of these orbitals are determined by solving Schrodinger’s wave equation. Schrodinger’s wave equation: The exact solution of the equation yields the four quantum numbers. These numbers are the electrons ‘address’. No two electrons in the atom have the exact same set of quantum number. Quantum Numbers Quantum numbers are needed to describe distribution of electron. There are three quantum numbers needed to this: Principal quantum number, Orbital-shape quantum number or angular momentum quantum number, magnetic quantum number, spin quantum number. Principle Quantum number (n) Indicated the size of the orbitals since it relates average distance of electron from nucleus in particular orbital. The bigger the n number the further away from nucleus an electron is. The number of electrons in the energy level can be determined 2n2 Orbital-Shape Quantum Number (l) Indicated shape/type of orbital l has possible integral values from 0 to (n –1): l=0: s orbital l=1: p orbital l=2: d orbital l=3: f orbital Principal Quantum # (n) 1 2 3 4 5 Orbital-Shape Quantum # (l) Orbital type Magnetic Quantum Number (ml) Indicates the direction/orientation of orbital in space. Indicates the number of orbitals in a subshell with a particular l value. Total number of orientations can be calculated using the formula (2l+1). Orientations can also be used by following this sequence: -l, (-l+1), …0, … (+l –1), +l or more simply integers from –l to +l. Spin Quantum Number (ms) Evidence for spin was based on the fact that lines of spectra split in the presence of an external magnetic field. Electrons act like tiny magnets, as the electrons spin on their own axis it generates a magnetic field of its own. In 1924, Stern and Gerlech proved the electron spin nature. Values are +1/2 or –1/2 Two electrons sharing a single orbital must have different spins (Pauli exclusion principle).