Question 28 of 32intermediate🔧 ApplyLong Answer3 marks

Use molecular orbital theory to explain why the Be₂ molecule does not exist.

Correct Answer

The electronic configuration of a beryllium atom is 1s22s21s^2 2s^2. In a Be2_2 molecule, there are 8 electrons. According to molecular orbital theory, these electrons are accommodated in bonding and antibonding molecular orbitals, giving Be2_2 the electronic configuration: (σ1s)2(σ∗1s)2(σ2s)2(σ∗2s)2(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 (\sigma^* 2s)^2.

The bond order for the Be2_2 molecule is calculated as 12(bonding electrons−antibonding electrons)\frac{1}{2}(\text{bonding electrons} - \text{antibonding electrons}). For Be2_2, this is 12(4−4)=0\frac{1}{2}(4 - 4) = 0.

A bond order of zero indicates that the stabilizing effect of the bonding molecular orbitals is completely cancelled out by the destabilizing effect of the antibonding molecular orbitals. Therefore, the Be2_2 molecule is unstable and does not exist.

Exercise: EXERCISES | Q: 4.35 | (Page 34)
For More Understanding

Explanation

The textbook context explicitly provides the molecular orbital configuration for Be2 as (σ1s)2 (σ1s)2 (σ2s)2 (σ2s)2. By applying the bond order formula demonstrated in the He2 example, the bond order of Be2 is calculated as 1/2(4-4) = 0. A bond order of zero implies no net bonding, making the molecule unstable and non-existent.

Solution Steps

  1. Step 1: Determine the total electrons in Be2_2 (4 from each Be atom = 8 electrons) and write its MO configuration: (σ1s)2(σ∗1s)2(σ2s)2(σ∗2s)2(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 (\sigma^* 2s)^2.

  2. Step 2: Calculate the bond order using the formula 12(bonding electrons−antibonding electrons)\frac{1}{2}(\text{bonding electrons} - \text{antibonding electrons}), which gives 12(4−4)=0\frac{1}{2}(4 - 4) = 0.

  3. Step 3: Conclude that since the bond order is zero, the Be2_2 molecule is unstable and does not exist.

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