Which is the correct statement ?

Options

A. `H_(2)^(+)` ion is more stable than `H_(2)` molecule
B. The bond dissociation energy for `H_(2)^(+)` ion is +ve
C. The bond order of `H_(2)^(+)` ion is 0.5 and hence `H_(2)^(+)` ion does not exist
D. The electron density along a line joining the two centres of the hydrogen nuclei in `H_(2)^(+)` will always be greater than at the corresponding points along a similar line for `H_(2)`

Explanation

To determine which statement is correct regarding the hydrogen molecules \( H_2 \) and \( H_2^+ \), we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement:** \( H_2^+ \) is more stable than \( H_2 \).

- **Analysis:** The stability of a molecule is directly related to its bond order. The bond order of \( H_2 \) is 1 (since it has 2 electrons in the bonding orbital), while the bond order of \( H_2^+ \) is 0.5 (since it has 1 electron in the bonding orbital). A higher bond order indicates greater stability. Therefore, \( H_2 \) is more stable than \( H_2^+ \).

**Conclusion:** This statement is **incorrect**.

### Step 2: Analyze the second statement
**Statement:** The bond dissociation energy of \( H_2^+ \) is positive.

- **Analysis:** The bond dissociation energy is the energy required to break a bond. Since \( H_2^+ \) has a bond order of 0.5, it does have a bond, albeit weaker than that of \( H_2 \). Therefore, the bond dissociation energy of \( H_2^+ \) is indeed positive.

**Conclusion:** This statement is **correct**.

### Step 3: Analyze the third statement
**Statement:** The bond order of \( H_2^+ \) is 0.5 and hence \( H_2^+ \) does not exist.

- **Analysis:** A bond order of 0.5 indicates that there is some bond interaction present, meaning \( H_2^+ \) does exist. A molecule is said to not exist only if its bond order is 0. Since \( H_2^+ \) has a bond order of 0.5, it does exist.

**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze the fourth statement
**Statement:** The electron density will always be more in \( H_2 \) as compared to \( H_2^+ \).

- **Analysis:** \( H_2 \) has 2 electrons, while \( H_2^+ \) has only 1 electron. Therefore, the electron density (which is the number of electrons per unit volume around the nuclei) is indeed greater in \( H_2 \) compared to \( H_2^+ \).

**Conclusion:** This statement is **correct**.

### Final Conclusion
The correct statements are:
- The bond dissociation energy of \( H_2^+ \) is positive.
- The electron density will always be more in \( H_2 \) as compared to \( H_2^+ \).

### Summary of Correct Statements
- The bond dissociation energy of \( H_2^+ \) is positive.
- The electron density is greater in \( H_2 \) than in \( H_2^+ \).