Question

If the subsidiary quantum number of a sub-energy level is $4$, then maximum and minimum values of spin multiplicities are:

• A. $9,1$
• B. $10,1$
• C. $10,2$
• D. $8,1$

Answer 1

Answer: (B)

$10,1$

Subsidiary quantum number of 4 indicates g orbital with 9 degenerated 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 $+\frac{1}{2}$ or $-\frac{1}{2}$ depending on the if the electron spins in the clockwise or anticlockwise direction.

If there is one electron in the g orbital, $S=+\frac{1}{2}$

For a pair of electrons in 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.

$S=\frac{1}{2}\times 9=4.5$

Multiplicity $=2S+2\times 4.5+1=10$

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.