Step 1: Determine the Electron Configuration of the Acetylide Ion (C22-)
The acetylide ion (C22-) consists of two carbon atoms, each contributing 6 electrons, and it has a -2 charge. Therefore, the total number of electrons is:
- Total electrons = 2 (from C) + 2 (from charge) = 14 electrons.
Step 2: Write the Molecular Orbital Diagram for C22-
The molecular orbital configuration for C22- can be derived from the molecular orbital theory. The order of filling for the molecular orbitals for diatomic carbon species is:
- σ(1s), σ*(1s), σ(2s), σ*(2s), σ(2p_z), π(2p_x), π(2p_y), π*(2p_x), π*(2p_y)
For C22-, the electron configuration will be:
- σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² σ(2p_z)² π(2p_x)² π(2p_y)²
Step 3: Calculate the Bond Order
The bond order can be calculated using the formula:
Bond Order = (Number of bonding electrons - Number of antibonding electrons) / 2
From the configuration:
- Bonding electrons = 10 (σ(1s)² + σ(2s)² + σ(2p_z)² + π(2p_x)² + π(2p_y)²)
- Antibonding electrons = 4 (σ*(1s)² + σ*(2s)²)
Now, substituting into the formula:
Bond Order = (10 - 4) / 2 = 3
Step 4: Determine the Magnetic Property
To determine the magnetic property, we look at the number of unpaired electrons. In the case of C22-, all electrons are paired in the molecular orbital configuration. Therefore, C22- is diamagnetic.
Step 5: Compare with Other Species
We need to find another species with the same bond order (3) and magnetic property (diamagnetic).
- The species that fits this description is the nitrosyl cation (NO+).
- The electron configuration for NO+ (which has 14 electrons) is similar, leading to a bond order of 3 and being diamagnetic.
Conclusion
The bond order and magnetic property of the acetylide ion (C22-) are the same as that of the nitrosyl cation (NO+).
Final Answer
The correct answer is: NO+ (Nitrosyl cation).
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: