Which of the following cannot he formed ?

Options

A. `He^(2+)`
B. `He^(oplus)`
C. `He`
D. `He_(2)`

Explanation

To determine which of the following cannot be formed among He2+, He+, He, and He2, we will use the principles of molecular orbital theory. Here's a step-by-step solution:

### Step 1: Understand Molecular Orbital Theory
Molecular orbital theory states that the stability of a molecule can be determined by calculating its bond order. The bond order is given by the formula:
\[ \text{Bond Order} = \frac{(N_b - N_a)}{2} \]
where \( N_b \) is the number of bonding electrons and \( N_a \) is the number of antibonding electrons. A positive bond order indicates that the molecule is stable and can exist, while a bond order of zero or negative indicates that the molecule cannot exist.

### Step 2: Analyze He2+
For He2+, we have:
- Total electrons = 2 (from He) - 1 (for the positive charge) = 1 electron.
- The molecular orbital configuration is: \( \sigma_{1s}^1 \).
- Bond order calculation:
\[ \text{Bond Order} = \frac{(1 - 0)}{2} = \frac{1}{2} \]
Since the bond order is positive, He2+ can exist.

### Step 3: Analyze He+
For He+, we have:
- Total electrons = 2 (from He) - 1 (for the positive charge) = 1 electron.
- The molecular orbital configuration is: \( \sigma_{1s}^1 \).
- Bond order calculation:
\[ \text{Bond Order} = \frac{(1 - 0)}{2} = \frac{1}{2} \]
Since the bond order is positive, He+ can exist.

### Step 4: Analyze He
For He, we have:
- Total electrons = 2 (from He).
- The molecular orbital configuration is: \( \sigma_{1s}^2 \).
- Bond order calculation:
\[ \text{Bond Order} = \frac{(2 - 0)}{2} = 1 \]
Since the bond order is positive, He can exist.

### Step 5: Analyze He2
For He2, we have:
- Total electrons = 2 (from He) + 2 (from the second He) = 4 electrons.
- The molecular orbital configuration is: \( \sigma_{1s}^2 \sigma_{1s}^2 \).
- Bond order calculation:
\[ \text{Bond Order} = \frac{(2 - 2)}{2} = 0 \]
Since the bond order is zero, He2 cannot exist.

### Conclusion
Based on the bond order calculations, the molecule that cannot be formed is **He2**.

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