Increasing order of bond length is

Options

A. `NO^(-)ltNOltNO^+ltO_2^-`
B. `O_2^(-) ltNOltNO^(-)ltO^+`
C. `O_2^(-)ltNO^(-)ltNOltNO^+`
D. `NO^+ltNOltNO^(-)ltO_2^(-)`

Answer

To determine the increasing order of bond length for the molecules NO-, NO, NO+, and O2-, we need to calculate the bond order for each molecule. The bond order can be calculated using the total number of electrons in each molecule. The bond order is inversely proportional to bond length, meaning that a higher bond order corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Identify the Total Number of Electrons:**
- **NO-**: Nitrogen (N) has 7 electrons and Oxygen (O) has 8 electrons. The negative charge indicates one additional electron.
- Total = 7 (N) + 8 (O) + 1 (extra electron) = 16 electrons.
- **NO**: Nitrogen has 7 electrons and Oxygen has 8 electrons. No charge means no additional electrons.
- Total = 7 (N) + 8 (O) = 15 electrons.
- **NO+**: Nitrogen has 7 electrons and Oxygen has 8 electrons. The positive charge indicates a loss of one electron.
- Total = 7 (N) + 8 (O) - 1 (lost electron) = 14 electrons.
- **O2-**: Each Oxygen atom has 8 electrons. The negative charge indicates one additional electron.
- Total = 8 (O) + 8 (O) + 1 (extra electron) = 17 electrons.

2. **Calculate the Bond Order:**
- Bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \]
- For simplicity, we can use the total number of electrons to determine the bond order:
- **NO+** (14 electrons): Bond order = 3
- **NO** (15 electrons): Bond order = 2.5
- **NO-** (16 electrons): Bond order = 2
- **O2-** (17 electrons): Bond order = 1.5

3. **Determine the Order of Bond Length:**
- Since bond order is inversely proportional to bond length, we can arrange the molecules in order of increasing bond length based on their bond orders:
- Highest bond order (shortest bond length) to lowest bond order (longest bond length):
- NO+ (Bond order = 3)
- NO (Bond order = 2.5)
- NO- (Bond order = 2)
- O2- (Bond order = 1.5)

4. **Final Order of Increasing Bond Length:**
- Therefore, the increasing order of bond length is:
- O2- > NO- > NO > NO+

### Summary of Increasing Order of Bond Length:
- O2- > NO- > NO > NO+