# ch40 - Chapter 40 1. The magnitude L of the orbital angular...

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1515Chapter 401. The magnitudeLof the orbital angular momentumLis given by Eq. 40-2:(1)L . On the other hand, the componentszLarezLm, where,...m . Thus, the semi-classical angle iscos/zLL. The angle is the smallestwhenm, or1coscos(1)(1)  .With5, we have1cos(5/30)24.1 .2. For a given quantum numbernthere arenpossible values of, ranging from 0 to1n. For eachthe number of possible electron states isN= 2(2+ 1). Thus the totalnumber of possible electron states for a givennis112002212.nnnNNnThus, in this problem, the total number of electron states isNn= 2n2= 2(6)2= 72.3. (a) We use Eq. 40-2:343413 311.055 10J s3.65 10J s.L (b) We use Eq. 40-7:zLm. For the maximum value ofLzsetm=. Thus3434max3 1.05510J s3.1610J s.zL4. For a given quantum numbernthere arenpossible values of, ranging from 0 ton– 1. For eachthe number of possible electron states isN= 2(2+ 1). Thus, thetotal number of possible electron states for a givennis112002212.nnnllNNn(a) In this casen= 4, which impliesNn= 2(42) = 32.
CHAPTER 401516(b) Nown= 1, soNn= 2(12) = 2.(c) Heren= 3, and we obtainNn= 2(32) = 18.(d) Finally,nNn22 282c h.5. (a) For a given value of the principal quantum numbern, the orbital quantum numberranges from 0 ton1. Forn= 3, there are three possible values: 0, 1, and 2.(b) For a given value of, the magnetic quantum numbermranges fromto. For1, there are three possible values: – 1, 0, and +1.6. For a given quantum numberthere are (2+ 1) different values ofm. For eachgivenmthe electron can also have two different spin orientations. Thus, the totalnumber of electron states for a givenis given byN= 2(2+ 1).(a) Now= 3, soN= 2(23 + 1) = 14.(b) In this case,= 2, which meansN= 2(22 + 1) = 10.(c) Here= 1, soN= 2(21 + 1) = 6.(d) Now= 0, soN= 2(20 + 1) = 2.7. (a) Using Table 40-1, we find= [m]max= 4.(b) The smallest possible value ofnisn =max+1+ 1 = 5.(c) As usual,ms 12, so two possible values.8. (a) Forl4, the greatest value ofmisml4.(b) Two states (ms 12) are available forml4.(c) Since there are 9 possible values form:+4, +3, +2, +1, 0, – 1, – 2, – 3, –4 and twopossible values forsm, the total number of state available in the subshelll4is 18.

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Atomic orbital, Principal quantum number
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