 # 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.

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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)

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

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)

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)

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.

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…

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

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)

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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