Question

For a given ion with a magnetic moment of 2.83 BM, determine the total spin (S) of all the unpaired electrons. Which of the following options represents the correct total spin:

(a) 2
(b) 1
(c) 3/2
(d) 1/2

Answer 1

The total spin (S) of the unpaired electrons for an ion with a magnetic moment of 2.83 Bohr Magnetons is calculated to be 3/2, using the relationship between the magnetic moment and the spin quantum number.

Step-by-step explanation:

The total spin (S) of the unpaired electrons for an ion with a magnetic moment of 2.83 Bohr Magnetons is calculated to be 3/2, using the relationship between the magnetic moment and the spin quantum number. The question involves determining the total spin (S) of all the unpaired electrons for a given ion with a magnetic moment of 2.83 Bohr Magnetons (BM).

The magnetic moment (μ) is related to the spin quantum number by the formula: μ = √[4S(S+1)]BM where S is the total spin quantum number. To solve for S, we take the square of the magnetic moment (2.832 = 8.0089), divide it by 4, and then subtract 1/4 to find S(S+1). That gives us a value of 1.7522, and by trial and error or mathematical calculation, we find that S = 3/2 fits this equation since 3/2(3/2+1) = 1.75. Therefore, the correct total spin is option (c) 3/2.