Calculate the number of `p_(pi)-d_(pi)` bond(s) present in `SO_(4)^(2-)` :

Explanation

To calculate the number of \( p_{\pi}-d_{\pi} \) bonds present in \( SO_4^{2-} \), we can follow these steps:

### Step 1: Understand the Structure of \( SO_4^{2-} \)
- The sulfate ion \( SO_4^{2-} \) consists of one sulfur atom and four oxygen atoms.
- The sulfur atom is in the center, and it forms bonds with the oxygen atoms.

### Step 2: Determine the Bonding in \( SO_4^{2-} \)
- In \( SO_4^{2-} \), sulfur can form two double bonds with two of the oxygen atoms and two single bonds with the other two oxygen atoms.
- The double bonds involve \( p_{\pi} \) and \( d_{\pi} \) bonding interactions.

### Step 3: Identify the Types of Bonds
- Each double bond between sulfur and oxygen involves:
- One \( p_{\pi} \) bond (from the oxygen's \( p \) orbital)
- One \( d_{\pi} \) bond (from the sulfur's \( d \) orbital)

### Step 4: Count the \( p_{\pi}-d_{\pi} \) Bonds
- Since there are two double bonds in \( SO_4^{2-} \), each contributing one \( p_{\pi}-d_{\pi} \) bond, we can conclude:
- Total number of \( p_{\pi}-d_{\pi} \) bonds = 2 (one from each double bond).

### Final Answer
- The total number of \( p_{\pi}-d_{\pi} \) bonds in \( SO_4^{2-} \) is **2**.

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