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Which one of the following species does not exist under normal conditions?
A
$Li_2$
B
$Be_2^+$
C
$Be_2$
D
$B_2$
Detailed Solution
A species exists only if its bond order, $\frac{N_b - N_a}{2}$, is greater than zero.
$Li_2$ (6 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2$; bond order = $\frac{4 - 2}{2} = 1$
$Be_2$ (8 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^2$; bond order = $\frac{4 - 4}{2} = 0$
$Be_2^+$ (7 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^1$; bond order = $\frac{4 - 3}{2} = 0.5$
$B_2$ (10 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^2\ \pi2p_x^1 = \pi2p_y^1$; bond order = $\frac{6 - 4}{2} = 1$
$Be_2$ has zero bond order, so it does not exist under normal conditions.
$Li_2$ (6 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2$; bond order = $\frac{4 - 2}{2} = 1$
$Be_2$ (8 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^2$; bond order = $\frac{4 - 4}{2} = 0$
$Be_2^+$ (7 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^1$; bond order = $\frac{4 - 3}{2} = 0.5$
$B_2$ (10 electrons): $\sigma1s^2\ \sigma^*1s^2\ \sigma2s^2\ \sigma^*2s^2\ \pi2p_x^1 = \pi2p_y^1$; bond order = $\frac{6 - 4}{2} = 1$
$Be_2$ has zero bond order, so it does not exist under normal conditions.