Calculate expression `(x+y+z)` for diatomic molecules.
where x=Total number of singly occupied molecular orbital (SOMO) in `O_(2)`.
y=Total number of singly occupied molecular orbital (SOMO) in `B_(2)`
z=Total number of singly occupied molecular orbital (SOMO) in `NO`.

Answer

To solve the problem, we need to calculate the total number of singly occupied molecular orbitals (SOMO) for the diatomic molecules \( O_2 \), \( B_2 \), and \( NO \). We will denote these values as \( x \), \( y \), and \( z \) respectively, and then find the expression \( x + y + z \).

### Step 1: Calculate \( x \) for \( O_2 \)

1. **Determine the total number of electrons in \( O_2 \)**:
- Oxygen has 8 electrons, so \( O_2 \) has \( 8 + 8 = 16 \) electrons.

2. **Write the molecular orbital electronic configuration**:
- The configuration for \( O_2 \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \pi_{2p_y}^*^1 \]

3. **Count the singly occupied molecular orbitals (SOMO)**:
- The \( \pi_{2p_x}^* \) and \( \pi_{2p_y}^* \) each have 1 electron, resulting in 2 SOMOs.
- Thus, \( x = 2 \).

### Step 2: Calculate \( y \) for \( B_2 \)

1. **Determine the total number of electrons in \( B_2 \)**:
- Boron has 5 electrons, so \( B_2 \) has \( 5 + 5 = 10 \) electrons.

2. **Write the molecular orbital electronic configuration**:
- The configuration for \( B_2 \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^1 \]

3. **Count the singly occupied molecular orbitals (SOMO)**:
- The \( \pi_{2p_x} \) and \( \pi_{2p_y} \) each have 1 electron, resulting in 2 SOMOs.
- Thus, \( y = 2 \).

### Step 3: Calculate \( z \) for \( NO \)

1. **Determine the total number of electrons in \( NO \)**:
- Nitrogen has 7 electrons and oxygen has 8 electrons, so \( NO \) has \( 7 + 8 = 15 \) electrons.

2. **Write the molecular orbital electronic configuration**:
- The configuration for \( NO \) is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \]

3. **Count the singly occupied molecular orbitals (SOMO)**:
- The \( \pi_{2p_x}^* \) has 1 electron, resulting in 1 SOMO.
- Thus, \( z = 1 \).

### Step 4: Calculate \( x + y + z \)

Now, we can sum the values:
\[ x + y + z = 2 + 2 + 1 = 5 \]

### Final Answer:
The value of the expression \( (x + y + z) \) is \( 5 \).

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