Which of the given ion below is isoelectronic with `CO_2` ?

Options

A. `N_2^+`
B. `N_2O`
C. `O_2^+`
D. `O_2^-`

Answer

To determine which of the given ions is isoelectronic with \( CO_2 \), we need to find the total number of electrons in \( CO_2 \) and compare it with the other ions.

### Step 1: Calculate the number of electrons in \( CO_2 \)

- Carbon (C) has an atomic number of 6, which means it has 6 electrons.
- Oxygen (O) has an atomic number of 8, which means each oxygen atom has 8 electrons. Since there are two oxygen atoms in \( CO_2 \), we multiply by 2.

Total electrons in \( CO_2 \):
\[ \text{Total electrons} = \text{Electrons from C} + 2 \times \text{Electrons from O} = 6 + 2 \times 8 = 6 + 16 = 22 \]

### Step 2: Calculate the number of electrons in each of the given ions

1. **For \( N_2^+ \)**:
- Nitrogen (N) has an atomic number of 7. For \( N_2 \), we have 2 nitrogen atoms.
- Total electrons = \( 2 \times 7 - 1 \) (since it has a +1 charge)
\[ \text{Total electrons} = 14 - 1 = 13 \]

2. **For \( N_2O \)**:
- Total electrons = \( 2 \times 7 + 8 \) (2 nitrogen atoms and 1 oxygen atom)
\[ \text{Total electrons} = 14 + 8 = 22 \]

3. **For \( O_2^+ \)**:
- Oxygen has 8 electrons. For \( O_2 \), we have 2 oxygen atoms.
- Total electrons = \( 2 \times 8 - 1 \) (since it has a +1 charge)
\[ \text{Total electrons} = 16 - 1 = 15 \]

4. **For \( O_2^- \)**:
- Total electrons = \( 2 \times 8 + 1 \) (since it has a -1 charge)
\[ \text{Total electrons} = 16 + 1 = 17 \]

### Step 3: Compare the number of electrons

Now, we compare the total number of electrons in each species with that of \( CO_2 \):

- \( CO_2 \): 22 electrons
- \( N_2^+ \): 13 electrons
- \( N_2O \): 22 electrons
- \( O_2^+ \): 15 electrons
- \( O_2^- \): 17 electrons

### Conclusion

The only species that is isoelectronic with \( CO_2 \) (having the same number of electrons, which is 22) is \( N_2O \).

**Final Answer**: \( N_2O \) is isoelectronic with \( CO_2 \).

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