Question

If the subsidiary quantum number of a subenergy level is 4. the maximum and minimum values of the spin multiplicities are:

• A. 9,1
• B. 10, 1
• C. 10, 2
• D. 4, -4

Answer 1

The correct option is B 10, 1

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.

Hence,option B is correct answer.