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QUANTUM NUMBERS “Energy changes within an atom are simply the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy” (Schrodinger) Electron waves are standing waves, which are called orbitals. Each orbital has a characteristic energy. 1) Principal Quantum Number (n) All orbitals having the same “n” are said to be in the same shell “n” primarily describes the energy and size of the orbital (wave) As “n” increases the energy of the orbital increases also. n = 1 2 3 4 5……. 2) Secondary Quantum Number (l) Each energy level is divided into sublevels. Each sublevel is represented by a particular value of “l”. “l” describes the shape of an orbital Each sublevel has a different shape and amount of energy. The higher the “l” value the greater the energy. The number of sublevels is equal to “n” l” values ranges from 0 to n -1 e.g. if n = 1 if n = 2 if n = 5 then then then l=0 l = 0 or 1 l = 0, 1, 2, 3, or 4 There is one sublevel There are two sublevels There are five sublevels the values of “l” have letter designations: l 0 letter s shape? 1 p 2 d 3 f 4 g 5… h 3. Magnetic Quantum Number (m) Each sublevel is subdivided into orbitals. Each orbital has a specific orientation in space represented by “m”. “m” also give the number of orbitals in a sublevel. “m” values range from “– l to +l” e.g. if l = 0, the s sublevel, Then m = 0 There is 1 orbital; 1 possible orientation in space if l = 1, the p sublevel, Then m = -1, 0 +1. There are 3 orbitals; 3 possible orientations in space if l = 2 , the d sublevel, Then m = -2, -1, 0, +1, +2. There are 5 orbitals; 5 possible orientations in space NOTE: Each orbital holds two electrons and occupies as much space as possible. sublevel s p d f # of orbitals one three five seven Maximum # of electrons 2 2,2,2 = 6 2, 2, 2, 2, 2 = 10 2, 2, 2, 2, 2, 2 = 14 Note: The principal quantum number(n) = the # of sublevels in an energy level = the # of orbitals in an energy level n2 2 = the total # of electrons/energy level 2n e.g. For n = 2, there are two types of sublevels (two “l” values ) Î s, p Since there are three “p” orbitals; we have a total of 4 orbitals (22 = 4) Since each orbital can hold a maximum of 2 electrons, we would have a total of 8 electrons in the second shell (2 * 22 = 8) 4. Spin Quantum Number (s) “s” indicates the direction of spin for the electron. There are only two directions, so s = +1/2 or –1/2 EXAMPLE: Write the complete set of quantum numbers that are possible for the electrons found in the 2p sublevel n = 2; l = 1; ml = -1, 0, 1; 2, 2, 2, 2, 2, 2, NOTE: 1, 1, 1, 1, 1, 1, ms = +1/2; -1/2 -1, +1/2 -1, -1/2 0, +1/2 0, -1/2 1, +1/2 1, -1/2 Every electron in an atom has it’s own unique set of quantum numbers (its own address)