Question

For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ______ number of unpaired electrons.

Answer 1

Correct Answer: 4

The magnetic moment of a complex is 4.9 B.M. Thus, unpaired electrons maybe 4. The expression for the magnetic moment is μ= \(\sqrt{n(n+2)}\)
​Substitute values in the above expression.
4.9= \(\sqrt{n(n+2)}\)
​24.01=n(n+2)
⇒ n=4.

So, the correct answer is 4.

Answer 2

Step 1: Using the formula for the magnetic moment. 
The magnetic moment (\( \mu \)) is related to the number of unpaired electrons (n) by the formula: \[ \mu = \sqrt{n(n+2)} \] where \( \mu \) is the magnetic moment in Bohr Magneton (BM) and \( n \) is the number of unpaired electrons. 
Step 2: Substituting the given value of magnetic moment.
We are given that \( \mu = 4.90 \, \text{BM} \). Substituting this value into the formula: \[ 4.90 = \sqrt{n(n+2)} \] 
Step 3: Solving for \( n \). 
Squaring both sides: \[ (4.90)^2 = n(n + 2) \] \[ 24.01 = n(n + 2) \] Expanding the equation: \[ 24.01 = n^2 + 2n \] Rearranging the equation: \[ n^2 + 2n - 24.01 = 0 \] Solving this quadratic equation for \( n \) gives: \[ n = 4 \] Thus, the metal ion has 4 unpaired electrons.