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 (\(Z^{**}\)) at the periphery of a chromium atom using Slater's rules, we will follow these steps:

### Step 1: Determine the Electronic Configuration of Chromium
The atomic number of chromium (Cr) is 24. The electronic configuration is:
- \(1s^2\)
- \(2s^2 2p^6\)
- \(3s^2 3p^6\)
- \(4s^1 3d^5\)

So, the complete electronic configuration can be written as:
\[ \text{Cr: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5 \]

### Step 2: Identify the Valence Electron
In chromium, the outermost electron is in the \(4s^1\) orbital. This is the electron for which we will calculate the effective nuclear charge.

### Step 3: Apply Slater's Rules to Calculate the Screening Constant (\(\sigma\))
According to Slater's rules, we need to calculate the screening constant (\(\sigma\)) for the \(4s^1\) electron as follows:

1. **Contribution from other electrons in the same group (valence shell)**:
- There is 1 electron in the \(4s\) orbital.
- According to Slater's rules, each electron in the same shell contributes \(0.35\).
- Contribution from \(4s^1\):
\[ 1 \times 0.35 = 0.35 \]

2. **Contribution from electrons in the \(3s\), \(3p\), and \(3d\) orbitals (inner shell)**:
- Total electrons in \(3s^2 3p^6 3d^5\) = \(2 + 6 + 5 = 13\).
- Each of these contributes \(0.85\).
- Contribution from \(3s, 3p, 3d\):
\[ 13 \times 0.85 = 11.05 \]

3. **Contribution from the \(1s\) and \(2s, 2p\) orbitals (inner shell)**:
- Total electrons in \(1s^2 2s^2 2p^6\) = \(2 + 2 + 6 = 10\).
- Each of these contributes \(1.00\).
- Contribution from \(1s\) and \(2s, 2p\):
\[ 10 \times 1.00 = 10.00 \]

### Step 4: Calculate the Total Screening Constant (\(\sigma\))
Now, we sum all contributions to find \(\sigma\):
\[ \sigma = 0.35 + 11.05 + 10.00 = 21.40 \]

### Step 5: Calculate the Effective Nuclear Charge (\(Z^{**}\))
The effective nuclear charge is calculated using the formula:
\[ Z^{**} = Z - \sigma \]
Where \(Z\) is the atomic number of chromium, which is 24:
\[ Z^{**} = 24 - 21.40 = 2.60 \]

### Final Answer
The effective nuclear charge at the periphery of a chromium atom is:
\[ \boxed{2.60} \]