The total number of species from the following in which one unpaired electron is present, is ____.
\[ \text{N}_2, \text{O}_2, \text{C}_2^{-}, \text{O}_2^{-}, \text{H}_2^{+}, \text{CN}^{-}, \text{He}_2^{+} \]
\[ \text{N}_2, \text{O}_2, \text{C}_2^{-}, \text{O}_2^{-}, \text{H}_2^{+}, \text{CN}^{-}, \text{He}_2^{+} \]
Correct Answer: 4
Approach Solution - 1
To determine the total number of species with one unpaired electron, we can use Molecular Orbital (MO) theory. Applying MO theory involves analyzing the electronic configurations and drawing the relevant conclusions about unpaired electrons:
- N2: The electronic configuration is \((1\sigma_g)^2(1\sigma_u^*)^2(2\sigma_g)^2(2\sigma_u^*)^2(3\sigma_g)^2(1\pi_u)^4(1\pi_g^*)^0\). No unpaired electrons.
- O2: The configuration is \((1\sigma_g)^2(1\sigma_u^*)^2(2\sigma_g)^2(2\sigma_u^*)^2(3\sigma_g)^2(1\pi_u)^4(1\pi_g^*)^2\). Two unpaired electrons are present (one in each \(\pi_g^*\) orbital).
- C2-: The configuration is \((1\sigma_g)^2(1\sigma_u^*)^2(2\sigma_g)^2(1\pi_u)^4(3\sigma_u)^0\). Adding one electron gives \((3\sigma_u)^1\), so one unpaired electron is present.
- O2-: The configuration is \((1\sigma_g)^2(1\sigma_u^*)^2(2\sigma_g)^2(2\sigma_u^*)^2(3\sigma_g)^2(1\pi_u)^4(1\pi_g^*)^3\). One unpaired electron remains in a \(\pi_g^*\) orbital.
- H2+: The configuration is \((1\sigma_g)^1\), which has one unpaired electron.
- CN-: This radical is isoelectronic with N2; \((1\sigma)^2(2\sigma)^2(1\pi)^4\). Therefore, there are no unpaired electrons.
- He2+: The configuration is \((1\sigma_g)^2(1\sigma_u^*)^1\). One unpaired electron is present.
Summing up, the species \(O_2, C_2^-, O_2^-, H_2^+, \text{ and } He_2^+\) each have one unpaired electron. The total number is 5.
Approach Solution -2
Step 1: Analyze each species for unpaired electrons
- N\(_2\): All electrons are paired.
- O\(_2\): Two unpaired electrons are present in antibonding orbitals.
- C\(_2^-\): One unpaired electron is present.
- O\(_2^-\): One unpaired electron is present.
- H\(_2^+\): One unpaired electron is present.
- CN\(^-\): All electrons are paired.
- He\(_2^+\): One unpaired electron is present.
Step 2: Count the species with one unpaired electron
Species with one unpaired electron:
\[ C_2^-, \, O_2^-, \, H_2^+, \, He_2^+. \]
Total number = 4.
Thus, the correct Answer is 4.
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