If `Z_("eff")`  of `F (Z=9)`  is X and `Z_("eff")` of `Li (Z = 3)` is Y then find the value of `|X-Y|` 

Options

A. `4.90`
B. `3.90`
C. `2.90`
D. `1.90`

Answer

To solve the problem of finding the value of \(|X - Y|\), where \(X\) is the effective nuclear charge (\(Z_{\text{eff}}\)) for fluorine and \(Y\) is the \(Z_{\text{eff}}\) for lithium, we will follow these steps:

### Step 1: Calculate \(Z_{\text{eff}}\) for Fluorine (F)
1. **Identify the atomic number of fluorine (Z):**
\(Z = 9\)

2. **Determine the electronic configuration of fluorine:**
The electronic configuration is \(1s^2 2s^2 2p^5\).

3. **Count the electrons in the outermost shell (N):**
The outermost shell (2nd shell) has 7 electrons (2 from \(2s\) and 5 from \(2p\)).

4. **Calculate the contribution (S) from the inner electrons:**
- For \(N\): \(0.35\) (for the outermost electron)
- For \(N - 1\): \(0.85\) (for the two electrons in \(1s\))
- For \(N - 2\): \(1\) (not applicable here since there are no electrons in \(N - 2\))

The total contribution \(S\) is calculated as follows:
\[ S = (6 \text{ electrons}) \times 0.35 + (2 \text{ electrons}) \times 0.85 = 2.1 + 1.7 = 3.8 \]

5. **Calculate \(Z_{\text{eff}}\) for fluorine:**
\[ Z_{\text{eff}} = Z - S = 9 - 3.8 = 5.2 \]
Thus, \(X = 5.2\).

### Step 2: Calculate \(Z_{\text{eff}}\) for Lithium (Li)
1. **Identify the atomic number of lithium (Z):**
\(Z = 3\)

2. **Determine the electronic configuration of lithium:**
The electronic configuration is \(1s^2 2s^1\).

3. **Count the electrons in the outermost shell (N):**
The outermost shell (2nd shell) has 1 electron.

4. **Calculate the contribution (S) from the inner electrons:**
- For \(N\): \(0.35\) (for the outermost electron)
- For \(N - 1\): \(0.85\) (for the two electrons in \(1s\))

The total contribution \(S\) is calculated as follows:
\[ S = (2 \text{ electrons}) \times 0.85 = 1.7 \]

5. **Calculate \(Z_{\text{eff}}\) for lithium:**
\[ Z_{\text{eff}} = Z - S = 3 - 1.7 = 1.3 \]
Thus, \(Y = 1.3\).

### Step 3: Calculate \(|X - Y|\)
Now, we find the absolute difference:
\[ |X - Y| = |5.2 - 1.3| = |3.9| = 3.9 \]

### Final Answer
The value of \(|X - Y|\) is \(3.9\).

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