In its ground state, carbon's 2pelectrons interact to produce jT=0. Given Hund's rule. what does this say about the total orbital angular momentum of these electrons?

Short Answer

Expert verified

Total orbital angular momentum isL=2h.

Step by step solution

01

Total spin of two electrons

The total spin of the two electronsSTis

ST=ST(ST+1)h ….(1)

02

total spin quantum number

The quantum number jT is zero jT=0.

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

By using Hund's rule, we conclude that the total spin quantum number st is given by

ST=s1+s2=12+12ST=1

03

total spin of electrons

By using Eq. (I), we find the total spin of the electrons sT as

ST=sTsT+1h=1.1+1hST=2h

04

The total orbital angular momentum LT

Now, since jT=0, we conclude that the total orbital angular momentum LT must be equal to the total spin ST

LT=ST=2h

Hence the total orbital angular momentum is LT=2h.

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