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Among the following molecules / ions $C_2^{2-} ,N_2^{2-} ,O_2^{2-},O_2$ which one is diamagnetic and has the shortest bond length ?
$O_2^{2-}$
$C_2^{2-}$
$O_2$
$N_2^{2-}$
Solution
$C_2^{2 – } – {\sigma _{1s}}2{\sigma ^*}_{1s}2{\sigma _{2s}}2{\sigma ^*}_{2{s^2}}[{\pi _{2p_x^2}} = {\pi _2}p_y^2]{\sigma _{2p_z^2}}$
$B.O = \frac{{10 – 4}}{2} = 3$ (diamagnetic)
$N_2^{2 – } – {\sigma _{1s}}2{\sigma ^*}_{1s}2{\sigma _{2s}}2{\sigma ^*}_{2{s^2}}[{\pi _{2p_x^2}} = {\pi _2}p_y^2]{\sigma _{2p_z^2}}[{\pi _{2p_x^1}} = {\pi ^*}_{2p_y^1}]$
$B.O = \frac{{10 – 6}}{2} = 2$ (paramagnetic)
$O_2^{2 – } – {\sigma _{1s}}2{\sigma ^*}_{1s}2{\sigma _{2s}}2{\sigma ^*}_{2s}2{\sigma _{2p_z^2}}[{\pi _{2p_x^2}} = {\pi _2}p_y^2]\,[{\pi _{2p_x^2}} = {\pi ^*}_2p_y^2]$
$B.O = \frac{{10 – 8}}{2} = 1$ (diamagnetic)
${O_2} – {\sigma _{1s}}2{\sigma ^*}_{1s}2{\sigma _{2s}}2{\sigma ^*}_{2s}2{\sigma _{2p_z^2}}\,[{\pi _{2p_x^2}} = {\pi _2}p_y^2]\,[{\pi _{2p_x^2}} = {\pi ^*}_2p_y^2]$
$B.O = \frac{{10 – 6}}{2} = 2$ (paramagnetic)
Similar Questions
Match $List-I$ with $List-II$.
| $List-I$ | $List-II$ |
| $(A)$ $\Psi_{ MO }=\Psi_{ A }-\Psi_{ B }$ | $(I)$ Dipole moment |
| $(B)$ $\mu=Q \times I$ | $(II)$ Bonding molecular orbital |
| $(C)$ $\frac{N_{b}-N_{a}}{2}$ | $(III)$ Anti-bonding molecualr orbital |
| $(D)$ $\Psi_{ MO }=\Psi_{ A }+\Psi_{ B }$ | $(IV)$ Bond order |
