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Bohr model 1. Electrons revolve around nucleus in circular paths, like planets around the sun. He called these paths orbits. 2. Each orbit has a specific energy and any electron in that orbit has that energy. 3. Orbits are therefore also energy levels. The closer to the nucleus, the lower the energy. Energy levels are numbered 1, 2, 3, etc., with one the closest to the nucleus. 4. Electrons can jump from one orbit to another, but not in between. In order for this jump to take place, energy has to be absorbed (going from low to high) or emitted (going from high to low) This last point explains absorption and emission spectra. Each possible jump will correspond to a specific energy and only that energy, which will correspond to a specific wavelength of electromagnetic radiation. Every element has slightly different values for their energy levels. Also, different atoms have different numbers of possible jumps. Bohr also showed that when an electron moves from one energy level to another, the energy emitted or absorbed follows the equation: 1 1 E h R H ( 2 - 2 ) ni nf RH is called the Rydberg Constant and has a value of 2.18 x 10-18J, and ni and nf are the initial and final Bohr energy levels. They are always integers. In the lab, you will do an experiment where the Rydberg constant is given a different value. The lab value incorporates h into the constant value, but we still call it the Rydberg constant. Not only does light have a dual nature, but so does all matter. It is only noticeable with very small particles, like the electron. In 1924, Louis de Broglie provided a mathematical explanation, which we won’t worry about. It is important to us only to show that photons are not unique, but that all matter is subject to the same rules of Nature. Although, the Bohr Model worked very well (actually exactly for the H atom) and was readily accepted as an advance in our knowledge of atomic structure, there were some theoretical problems that he could not really explain. It wasn’t until 1923, when a physical chemist, named Irwin Schrodinger, proposed a new model for the atom. This model is called the Quantum Mechanical Model. It is purely a mathematical model, but we can use the Bohr model with some liberal modifications, to help understand this model. Once again, like the Bohr Model, it can be solved exactly for the H atom, but not for multi-electron systems. However, we apply the assumptions for the H atom to any system, assuming that the differences will be small. Basic Assumptions: 1. Energies of electrons can have only specific values - similar to Bohr Model - quantized energies of electrons 2. Position cannot be specified - only most probable average position can be calculated 3. The solution of the mathematical Equation, called the Schrodinger Equation, requires certain values, called quantum numbers. There are 4 of these. They can only have certain restricted values, hence the term quantum numbers. Every electron in an atom has a set of these 4 quantum numbers, in order to completely describe its energy, as accurately as we can. Orbital - a part of a sublevel that actually contains the electrons (like cars on a road) - can hold a maximum of 2 electrons. The Principle Quantum Number – n: Describes the main energy level (like Bohr’s energy levels). It can only have positive integer values (1, 2,3 etc). Like the Bohr Model Energy Levels, the higher the n value, the higher the energy and the further away from the nucleus. The Angular Momentum Quantum Number – (l): Describes the shape of the orbitals. Also describes the energy of sublevels to the principle energy level. The values of l are dependent on the value of n. For each value of n, l can have integer values from 0 to n-1. Chemists have found it convenient to assign letters for each different l value: l value Letter Symbol 0 s 1 p 2 d 3 f The lower the value, the lower the energy. The Magnetic Quantum Number – (ml) Describes the orientation of an orbital in space. Also describes the energy of the electron, if it is subject to external magnetic fields. In ordinary situations, the energy of the electron is the same for all values of ml corresponding to a certain l value. ml values are restricted to all integers, including 0, from – l to + l The Electron Spin Quantum Number - (ms) Essentially describes the direction of spin for the electron (clockwise or counterclockwise). Enables 2 electrons to occupy the same orbital. Has no effect on the energy of the electron unless there is an external magnetic field. Can have values of + ½ or – ½ . Examples: If n = 1, then l = 0, ml = 0 and ms = + ½ or – ½ . Frequently abbreviated as (1,0,0,+ ½ ) or (1,0,0, - ½ ). If n =3, then l can be 0, 1, or 2. The values of ml depend on which l value we refer to: for 0, then ml can only be 0; for l = 1, ml can be -1, 0 or +1; and for l = 2, ml can be -2,-1,0,+1 or +2. Each different ml represents a different orbital and each orbital can have ms values of + ½ or – ½ . Thus for n = 3, there are 9 possible different orbitals. TABLE 7-1 l n ml # of orbitals Maximum # of electrons 1 0 0 1 2 2 0 0 1 2 1 -1,0,+1 3 6 0 0 1 2 1 -1,0,+1 3 6 2 -2,-1,0,+1,+2 5 3 10 Orbital Shapes: