For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ______ number of unpaired electrons.
Correct Answer: 4
Approach Solution - 1
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.
Approach Solution -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.
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Concepts Used:
D and F Block Elements
The d-block elements are placed in groups 3-12 and F-block elements with 4f and 5f orbital filled progressively. The general electronic configuration of d block elements and f- block elements are (n-1) d 1-10 ns 1-2 and (n-2) f 1-14 (n-1) d1 ns2 respectively. They are commonly known as transition elements because they exhibit multiple oxidation states because of the d-d transition which is possible by the availability of vacant d orbitals in these elements.
They have variable Oxidation States as well as are good catalysts because they provide a large surface area for the absorption of reaction. They show variable oxidation states to form intermediate with reactants easily. They are mostly lanthanoids and show lanthanoid contraction. Since differentiating electrons enter in an anti-penultimate f subshell. Therefore, these elements are also called inner transition elements.
Read More: The d and f block elements