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Chapter 8: 79E (page 344)

In its ground state, nitrogen's 2p electrons interact to produce jT=32. Given Hund's rule, how might the orbit at angular momenta of these three electrons combine?

Short Answer

Expert verified

The total orbital quantum number lT arelT=0,1,2,3.

Step by step solution

01

total spin

The total spin STis given by

ST=sT(sT+1)h

02

total quantum number

The total quantum number jT is jT=32.

03

total spin quantum number

The spin quantum number of each electron is s1=s2=s3=12.

By using Hund's rule, we find the total spin quantum number sT as

sT=s1+s2+s3=12+12+12sT=32

04

the total orbital quantum number lT

Now, the 'candidates' for the total orbital quantum number lT are

lt=0,1,2,3

05

observation

As we see from the values of jT and sT, all of the 'candidates' for lT are possible, since the difference between them and the total quantum number jT is not greater than32 (the rules of addition of the angular momenta are satisfied).

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