The sum of the number of lone pair of electrons on each central atom in the following species is
`[TeBr_(6)]^(2-), [BrF_(2)]^(2+), SNF_(3), and [XeF_(3)]^(-)`
(Atomic number : N = 7, F = 9, S = 16, Br = 35, Te = 52, Xe = 54)

Explanation

To find the sum of the number of lone pairs of electrons on each central atom in the given species, we will analyze each species one by one.

### Step 1: Analyze [TeBr₆]²⁻
1. **Valence Electrons Calculation**:
- Tellurium (Te) has 6 valence electrons.
- The charge of -2 means we add 2 more electrons.
- Total valence electrons for Te = 6 + 2 = 8.

2. **Bonding with Bromine (Br)**:
- Each Bromine contributes 1 electron for bonding.
- With 6 Br atoms, we use 6 electrons for 6 bond pairs.

3. **Lone Pairs Calculation**:
- Total electrons = 8 (from Te) - 6 (used in bonding) = 2 electrons left.
- These 2 electrons form 1 lone pair.

**Lone pairs on Te = 1**

### Step 2: Analyze [BrF₂]²⁺
1. **Valence Electrons Calculation**:
- Bromine (Br) has 7 valence electrons.
- The charge of +2 means we subtract 2 electrons.
- Total valence electrons for Br = 7 - 2 = 5.

2. **Bonding with Fluorine (F)**:
- Each Fluorine contributes 1 electron for bonding.
- With 2 F atoms, we use 2 electrons for 2 bond pairs.

3. **Lone Pairs Calculation**:
- Total electrons = 5 (from Br) - 2 (used in bonding) = 3 electrons left.
- These 3 electrons form 1 lone pair (2 electrons) and 1 single electron (which does not form a lone pair).

**Lone pairs on Br = 1**

### Step 3: Analyze SNF₃
1. **Valence Electrons Calculation**:
- Sulfur (S) has 6 valence electrons.
- Nitrogen (N) has 5 valence electrons.
- Each Fluorine (F) has 1 valence electron.
- Total = 6 (S) + 5 (N) + 3 (F) = 14 valence electrons.

2. **Bonding**:
- N forms 3 bonds with 3 F atoms using 3 electrons.
- S forms a double bond with N using 2 electrons.

3. **Lone Pairs Calculation**:
- Total electrons = 14 - (3 + 2) = 9 electrons left.
- N has no lone pairs, and S has 4 electrons left, which forms 2 lone pairs.

**Lone pairs on S = 2**

### Step 4: Analyze [XeF₃]⁻
1. **Valence Electrons Calculation**:
- Xenon (Xe) has 8 valence electrons.
- The charge of -1 means we add 1 more electron.
- Total valence electrons for Xe = 8 + 1 = 9.

2. **Bonding with Fluorine (F)**:
- Each Fluorine contributes 1 electron for bonding.
- With 3 F atoms, we use 3 electrons for 3 bond pairs.

3. **Lone Pairs Calculation**:
- Total electrons = 9 (from Xe) - 3 (used in bonding) = 6 electrons left.
- These 6 electrons form 3 lone pairs.

**Lone pairs on Xe = 3**

### Final Calculation:
Now, we sum the lone pairs from each central atom:
- Lone pairs on Te = 1
- Lone pairs on Br = 1
- Lone pairs on S = 2
- Lone pairs on Xe = 3

**Total lone pairs = 1 + 1 + 2 + 3 = 7**

### Answer:
The sum of the number of lone pairs of electrons on each central atom in the species is **7**.