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Quantum Mechanics:

Quantum Mechanics:. the sequel . 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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Quantum Mechanics:

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  1. Quantum Mechanics: the sequel

  2. Quantum Numbers • Read on pg. 200 from “The theory of quantum…” (about third paragraph) to “The Magnetic Quantum Number, ml” 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)

  3. ml : the magnetic quantum number • Recall: we are looking at the first three of four quantum numbers: n, l, ml, ms • The magnetic quantum number is ml, 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 • ml ranges from - l to + l, in intervals of one • when l = 1, the values of ml are -1, 0, 1

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

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

  6. 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 2n2 : 2(3)2 = 18. • From now on, you can determine the # of electrons in a shell by using this “2n2” rule.

  7. 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…

  8. 4d 5s E N E R G Y 4p 3d 4s 3p 3s 2p 2s 1s

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

  10. ms : the final quantum number! • Recall: the quantum numbers: n, l, ml, ms • The spin quantum number is ms, 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 ms is + 1/2 or - 1/2 • Don’t worry about why they are fractions • The important point is that there are two values. It’s important because … For more lessons, visit www.chalkbored.com

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