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Quantum Mechanics: the sequel

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Quantum Numbers Read on pg. 200 from The theory of quantum… (about third paragraph) to The Magnetic Quantum Number, m l on pg. 201. Do PE 3 The subshells of n = 3 are l = 0(s), 1(p), 2(d) for n = 4: l = 0(s), 1(p), 2(d), 3(f)

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m l : the magnetic quantum number Recall: we are looking at the first three of four quantum numbers: n, l, m l, m s The magnetic quantum number is m l, it further divides subshells into orbitals Recall that even though you can visualize these divisions as spherical regions around the nucleus, they really refer to different waveforms m l ranges from - l to + l, in intervals of one when l = 1, the values of m l are -1, 0, 1

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m l : the magnetic quantum number Read the remainder of 201. What is m l when l = 3 (f)? When l = 0 (s)? l = 3 (f) m l = -3, -2, -1, 0, 1, 2, 3 (l = 0 (s) m l = -0, 0 which is just 0 so … ) l = 0 (s) m l = 0 PE 4: How many orbitals are in a g subshell? g means l = 4, thus m l = -4,-3,-2,-1,0,1,2,3,4 (9 orbitals all together)

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m l : the magnetic quantum number What is m l when l = 3 (f), when l = 0 (s) l = 3 (f) m l = -3, -2, -1, 0, 1, 2, 3 l = 0 (s) m l = -0, 0 which is just 0 so … l = 0 (s) m l = 0 Read the remainder of 201. Do PE 4. g means l = 4, thus m l = -4,-3,-2,-1,0,1,2,3,4 (9 orbitals all together)

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More practice with quantum #s Complete the chart on the study sheet Look at the last two columns of the chart. A maximum of two electrons can fit in each orbital. For n = 3, a maximum of 18 electrons can fit in this shell (2 + 6 + 10) This is equivalent to 2n 2 : 2(3) 2 = 18. From now on, you can determine the # of electrons in a shell by using this 2n 2 rule.

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Summary Read pg. 202 Figure 6.19 indicates the energies of subshells and the number of orbitals in each. We will see that each of these orbitals can hold exactly 2 electrons Note that some shells overlap with respect to energy. If we extend a Bohr-like model to represent this we would see shells being split into subshells causing some shells to overlap…

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5s 4s 3s 2s 1s 2p 3p 4p 3d 4d ENERGYENERGYENERGYENERGY

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The overlapping of subshells n = 1 n = 2 n = 3 n = 4 To visualize what is happening we are equating energy of a subshell to size Note: not exactly to scale (see fig. 6.19)

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m s : the final quantum number! Recall: the quantum numbers: n, l, m l, m s The spin quantum number is m s, it can be thought of as the clockwise vs. counterclockwise spin of an electron (as on pg. 203, or as a waveform)… The value of m s is + 1/2 or - 1/2 Dont worry about why they are fractions The important point is that there are two values. Its important because … For more lessons, visit www.chalkbored.com www.chalkbored.com

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