If the subsidiary quantum number of a subenergy level is 4, the maximum and minimum values of spin multiplicities are :
a) 9,1
b)10,1
c) 10,2
d) 4,-4
Could you please explain what's spin multiplicity?

Dear Student,

Please find below the solution to the asked query:

Subsidiary quantum number of 4 indicates g orbital with 9 degenerate sub- orbitals. The orbital can take up a maximum of  18 electrons.
The spin multiplicity value, is given by the formula 2S + 1
Where,  S is the sum of spins of the electrons. Spin of an electron is either +1/2  or -1/2 depending on the if the electron spins in the clockwise or anticlockwise direction.
If there is one electron in the g orbital, S = +1/2
For a pair of electrons in a g sub-orbital, the spin quantum number cancels out.
So, unpaired electrons effectively contribute to spin multiplicity.
The maximum value will be given by 9 unpaired electrons with positive spin.
S = 9 $\times$ ½ = 4.5
Multiplicity = 2S + 1 = 2 $\times$ 4.5 + 1 = 10
The minimum value will be given when  no unpaired electron is present
S = 0
Multiplicity = 2 $\times$ 0+ 1 = 1
So, maximum and minimum values are 10. 1 (option b)
 
Multiplicity indicates the various possible quantum states of a system with the principal spin quantum number S and is given by the formula 2S + 1.
S is the sum of the spin of electrons.
For example, O is the electronic configuration 1s² 2s² 2p⁴
For p orbital, there are 4 electrons with spins, +1/2, +1/2, +1/2 and -1/2 and
S = ½ + ½ + ½ -1/2 = 1
 
 

Hope this information will clear your doubts about spin multiplicity.

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