J.C. Slater proposed an empirical constant that represents the cumulative extent to which the other electrons of an atom shield (or screen) any particular electron from the nuclear charge. Thus, slater's screening contant `sigma` is as : `Z^(**)=Z-sigma`
Here, Z is the atomic number of the atom, and hence is equal to the actual number of protons in the atom. the parameter `Z^(**)` is the effective nuclear charge, which according to is smaller than Z, since the electron in question is screened (shielded) from Z by an amount `sigma`. Conversely, an electron that is well shielded from the nuclear charge Z experiences a small effective nuclear charge `Z^(**)`.
The value of `sigma` for any one electron in a given electron configuration (i.e., in the presence of the other electrons of the atom in question) is calculated using a set of empirical rules developed by slater. according to these rules, the value of `sigma` for the electron in question is the cumulative total provided by the various other electrons of the atom.
Q. The effective nuclear charge at the periphery of chromium atom [Z=24]:

Options

A. 4.25
B. 2.6
C. 3.6
D. 1.21

Explanation

To calculate the effective nuclear charge (\(Z^{**}\)) for the outermost electron of a chromium atom (atomic number \(Z = 24\)), we will use Slater's rules to determine the screening constant (\(\sigma\)).

### Step-by-Step Solution:

1. **Identify the Electron Configuration**:
The electron configuration of chromium is \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^1\). However, due to the stability of half-filled subshells, we can represent it as \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^1\).

2. **Assign Electrons to Shells**:
- The outermost electron is in the 4s orbital.
- The electrons in the same shell (4s) are considered as \(n\).
- The electrons in the previous shell (3s, 3p, 3d) are considered as \(n-1\).
- The electrons in the shells before that (1s, 2s, 2p) are considered as \(n-2\).

3. **Count the Electrons**:
- For \(n\) (4s): There is 1 electron (4s^1).
- For \(n-1\) (3s, 3p, 3d): There are 2 (3s) + 6 (3p) + 5 (3d) = 13 electrons.
- For \(n-2\) (1s, 2s, 2p): There are 2 (1s) + 2 (2s) + 6 (2p) = 10 electrons.

4. **Calculate the Screening Constant (\(\sigma\))**:
Using Slater's rules:
- Each electron in the same shell (4s) contributes 0.35.
- Each electron in the \(n-1\) shell (3s, 3p, 3d) contributes 0.85.
- Each electron in the \(n-2\) shell contributes 1.

Therefore, the calculation for \(\sigma\) is:
\[ \sigma = (1 \times 0.35) + (13 \times 0.85) + (10 \times 1) \]
\[ \sigma = 0.35 + 11.05 + 10 = 21.40 \]

5. **Calculate the Effective Nuclear Charge (\(Z^{**}\))**:
Now, we can find the effective nuclear charge using the formula:
\[ Z^{**} = Z - \sigma \]
Substituting the values:
\[ Z^{**} = 24 - 21.40 = 2.60 \]

### Final Answer:
The effective nuclear charge at the periphery of a chromium atom is \(Z^{**} = 2.60\).