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Quantum numbers Where Does Tin-Tin Live? http://www.epa.gov/kidshometour/images/house.jpg Where Does Tin-Tin Live? Tin-Tin lives in a dorm in a condominium unit. In the dorm, there are male and female sections per floor. Per room, there are only two beds. If asked where EXACTLY she lives, how would she answer? Prince David Condominium in Katipunan Ave 3rd floor Female section Room 314 Bed near window The quantum mechanical model answers the question, “Where does the electron live?” Prince David Condominium in Katipunan Ave The electron belongs to chlorine 3rd floor 3rd energy level (n=3) Female section In the p-subshell (l=1) Room 314 In one of the three degenerate orbitals eg. ml= 0 Bed near window Electron is spin-up eg. ms= +1/2 The quantum mechanical model answers the question, “Where does the electron live?” • • Three quantum numbers describe the electron’s address 1. principal quantum number (n) 2. angular momentum quantum number (l) 3. magnetic quantum number (ml) A fourth quantum number is added to pinpoint the location 4. spin quantum number (ms) Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The principal quantum number (n) gives the distance of the e- from the nucleus n=3 n=1 n=2 n = 1, 2, 3, 4, …. The larger the n, the larger the average distance of the e- from the nucleus Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The values of the angular momentum quantum number (l) depend on n for a given value of n, l = 0, 1, 2, 3, … n-1 Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The values of the angular momentum quantum number (l) depend on n Silberberg, M. 2010. Principles of General Chemistry. 2nd ed. New York: McGraw-Hill. The angular momentum quantum number (l) gives the shape of the orbital l 0 1 2 3 Name of Orbital s p d f Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The angular momentum quantum number (l) gives the shape of the orbital l=0 s orbital Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The angular momentum quantum number (l) gives the shape of the orbital l=1 p orbital Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The angular momentum quantum number (l) gives the shape of the orbital l=2 d orbital Silberberg, M. 2010. Principles of General Chemistry. 2nd ed. New York: McGraw-Hill. The angular momentum quantum number (l) gives the shape of the orbital l=3 f orbital http://int.ch.liv.ac.uk/Lanthanide/Graphics/f-orbs.gif The value of the magnetic quantum number (ml) depends on l for a given value of l, ml = l, …., 0, …. -l Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. Silberberg, M. 2010. Principles of General Chemistry. 2nd ed. New York: McGraw-Hill. The magnetic quantum number (ml) describes the orientation of the orbital in space ml = +1 ml = 0 ml = -1 Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. The spin quantum number (ms) accounts for an electron’s ability to act like tiny magnets ms = +½ ms = -½ Chang, R. 2002. Chemistry 7th ed. Singapore: McGraw-Hill. Terms to remember • Shell – electrons with the same values of n • Subshell – electrons with the same values of n and l • Orbital – electrons with the same values of n, l, and ml – an orbital can hold at most two electrons Note that the orbitals are just spaces—it does not mean that an electron occupies the entire space at any given time Test Your Understanding • For n = 4, what are the possible combinations of l and ml? l=0 l=2 ml = 0 ml = -2, -1, 0, +1, +2 l=1 l=3 ml = -1, 0, +1 ml = -3, -2, -1, 0, +1, +2, +3 Test Your Understanding Which of the following are permissible sets of quantum numbers for an electron (n, l, ml)? If permissible, write the subshell to which it belongs 1. (2, 2, -2) Not permissible 2. (4, 3, -1) Permissible, 4f 3. (1, 0, 0) Permissible, 1s 4. (6, 3, -4) Not permissible