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SCH4U1 The Quantum Number System As we have seen, the location of an electron can be identified by its orbital type. These names indicate the energy level, shape and orientation of the electron. For example: 1s, 2px, 5dxy. Another system used to identify am electron is the quantum number system. With this system, a particular electron is designated by a set of 4 numbers. Principal Quantum Number (n) This indicates the energy level of the electron. n=1, 2, 3, 4, 5 etc. Secondary Quantum Number (l) Ranges from 0 to n-1 This indicates the shape or sublevel of the orbital the electron is in. l =0 (s orbital) l = 1 (p orbital) l = 2 (d orbital) l = 3 (f orbital) Magnetic Quantum Number (ml) This indicates the orientation of the orbital that the electron is in. Ranges from – l to +l. When l =0 ml = 0 (only 1 spherical orientation) When l = 1 ml = +1 (px), ml = 0 (py), ml = -1 (pz) (3 possible orientations) When l = 2 ml = +2, +1, 0, -1, -2 (5 possible orientations) When l = 3 ml = +3, +2, +1, 0, -1, -2, -3 (7 possible orientations) Spin Quantum Number (ms) Each orbital can contain 2 electrons. However these 2 electrons must have opposite spin. These are the same for all orbitals. ms = + ½ and - ½ Examples: What are the possible quantum numbers of an electron in the following orbitals: a) 1s b) 2px c) 5dxy Note that no 2 electrons in an atom can have the same 4 quantum numbers. SCH4U1 Energy Level Diagrams This is a useful tool to visualize orbitals and their relative energies. Electrons are added to an energy level diagram using the same rules described for writing electron configurations. Rules for drawing energy level diagrams: 1. Pauli Exclusion Principle: Represent each electron by an arrow. The direction of the arrow represents the electron spin. Draw an up arrow to show the first electron in each orbital. 2. Aufbau Principle: Electrons (arrows) are placed into the orbitals by filling the lowest energy orbitals first. An energy sublevel must be filled before moving on to the next higher level 3. Hund’s Rule: Place one electron into each orbital of the same energy before pairing the electrons. An aufbau diagram (right) is one way to memorize the order in which energy levels are filled. The diagonal arrows indicate the order in which electrons are added to the various orbitals. Examples: a) Carbon b) Manganese (leave lots of room) c) Neodynium SCH4U1 Electron Configurations of Ions Anions (negatively-charged ions) can be written simply by adding the number of electrons corresponding to the ionic charge and then drawing the electron configuration. Eg. Draw the electron configurations for the following: fluorine atom has 9 electrons, therefore the fluoride ion (F-) has 10 fluorine atom (F): fluoride ion (F-): Cations (positively-charged ions) can be written by first drawing the neutral atom and then removing electrons. e.g. sodium atom (Na) sodium ion (Na+) Note that the fluoride ion, neon atom and sodium ion are all isoelectronic (i.e. they have the same electron configurations). Draw the neon electron configuration and explain why based on your previous knowledge of formation of ions. Transition Metals: Bohr’s model could not explain the charges of the transition metals. The stable ions of iron can finally be explained by looking at their energy level diagrams. Electrons are always removed from the orbital with the highest principal quantum number first. e.g. iron atom (Fe): iron ion (Fe2+): iron ion (Fe3+): SCH4U1 Quantum Number and Energy Level Practice 1. Draw energy level diagrams for: a. a) F b) Ca c) Co 2. Write the short form electron configuration for: b. a) F b) Ca c) Co d) Yb e) N3- d) Yb 3. Identify the orbital corresponding to the following quantum numbers: a) n = 3, l = 2, ml = 1, ms = ½ b) n = 5, l = 3, ml = -3, ms = ½ c) n = 4, l = 1, ml = -1, ms = ½ d) n = 2, l = 1, ml = 0, ms = ½ e) n = 4, l = 2, ml = -2, ms = ½ 4. Which of the following designations are orbitals that are not possible in wave mechanics? c. 1d, 4f, 1p, 6d, 2f 5. Which of the following are sets of quantum numbers for orbitals are possible in wave mechanics? If they are not possible, explain why. d. a) n = 1, l = 1, ml = 1, ms = ½ d) n = 3, l = 3, ml = 1, ms = ½ e. b) n = 2, l = 1, ml = 2, ms = ½ e) n = 3, l = 2, ml = -2, ms = ½ f. c) n = 2, l = 0, ml = 0, ms = ½ f) n = 4, l = 3, ml = 2, ms = ½ 6. Write the quantum numbers for the two electrons in a 3s orbital. 7. a) The actual electron configuration of copper is [Ar]4s13d10 which is different from its expected configuration. Read p. 168 to explain this anomalous electron configuration. b) Draw chromium’s electron configuration and predict how it achieves its anomalous electron arrangement of [Ar]4s13d5. (look up the definition for anomaly if you don’t understand what the question is asking) 8. The last electron represented in an electron configuration is related to the position of the element in the periodic table. For each of the following sections of the periodic table, indicate the sublevel (s, p, d, f) of the last electron: a) groups 1 and 2 b) groups 3-12 (transition metals) c) groups 13-18 d) lanthanides and actinides 9. a) When the halogens form ionic compounds, what is the ionic charge of the halide ions? b) Describe and explain the similarities and differences in properties of these two chemical entities. 10. The sodium ion and the neon atom are isoelectronic: i.e., have the same electron configuration. a) Write the electron configurations for the sodium ion and the neon atom. b) Describe and explain the similarities and differences in properties of these two chemical entities. 11. Use energy level diagrams to explain the common ion charges for antimony, i.e., Sb3+, Sb5+. 12. Predict the electron configuration for the gallium ion, Ga3+. Provide your reasoning.