For a metal ion, the calculated magnetic moment is $4.90 ~\mathrm{BM}$. This metal ion has ___________ number of unpaired electrons.
Answer (integer)
4
Solution
<p>Using the equation $\mu = \sqrt{n(n+2)}$, where $\mu$ is the magnetic moment and $n$ is the number of unpaired electrons, we can substitute $\mu = 4.90$:</p>
<p>$4.90 = \sqrt{n(n+2)}$</p>
<p>Squaring both sides of the equation:</p>
<p>$(4.90)^2 = n(n+2)$</p>
<p>$24 = n^2 + 2n$</p>
<p>Rearranging the equation:</p>
<p>$n^2 + 2n - 24 = 0$</p>
<p>Solving the quadratic equation, we find:</p>
<p>$n =4$</p>
<p>Therefore, the metal ion has 4 unpaired electrons.</p>
About this question
Subject: Chemistry · Chapter: Coordination Compounds · Topic: Ligands and Coordination Number
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