Effective nuclear charge `(Z_(eff))` is the net attractive force on electrons under consideration and is equal to:
`Z_(eff) = Z - sigma` (nuclear charge - screening constant). `Z_(eff)` or `sigma` is calculated by Slater's formula, as given.
If one electrons is present in the outermst orbit, there will be no screening in that orbital. Each electrons contribute, `0.35` (total electrons minus one electron) present in the outermost shell.
A contribution of `0.85` for each electrons is taken in the `(n - 1)th` shell.
The screening constant `(sigma)` for `4s` electron of `Mn (Z = 25)` will be

Options

A. `18.00`
B. `4.25`
C. `18.35`
D. `22.6`

Explanation

To calculate the screening constant (σ) for the 4s electron of manganese (Mn, Z = 25), we will follow the steps outlined below:

### Step 1: Write the electronic configuration of manganese (Mn).
The atomic number of manganese is 25. Its electronic configuration is:
\[ \text{Mn: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^2 \]

### Step 2: Identify the electrons contributing to the screening constant (σ).
For the 4s electron, we consider the contributions from:
- Electrons in the inner shells (1s, 2s, 2p, 3s, 3p, and 3d).
- Electrons in the same shell (4s).

### Step 3: Calculate the contribution from the inner shell electrons.
The total number of inner shell electrons is:
\[ 2 \, (1s) + 2 \, (2s) + 6 \, (2p) + 2 \, (3s) + 6 \, (3p) + 5 \, (3d) = 2 + 2 + 6 + 2 + 6 + 5 = 23 \]
However, due to the poor shielding effect of the d electrons, we consider only the electrons in the inner shells (1s, 2s, 2p, 3s, and 3p) for full shielding:
\[ 2 + 2 + 6 + 2 + 6 = 18 \]
These contribute 1 unit each, so:
\[ \text{Contribution from inner shell} = 18 \times 1 = 18 \]

### Step 4: Calculate the contribution from the (n-1)th shell (3d electrons).
Each of the 5 electrons in the 3d subshell contributes 0.85:
\[ \text{Contribution from 3d} = 0.85 \times 5 = 4.25 \]

### Step 5: Calculate the contribution from the outermost shell (4s).
Since there is 1 electron in the outermost shell (4s), it contributes:
\[ \text{Contribution from 4s} = 0.35 \times 1 = 0.35 \]

### Step 6: Calculate the total screening constant (σ).
Now, we can sum up all contributions to find σ:
\[ σ = \text{Contribution from inner shell} + \text{Contribution from 3d} + \text{Contribution from 4s} \]
\[ σ = 18 + 4.25 + 0.35 = 22.6 \]

### Final Answer:
The screening constant (σ) for the 4s electron of manganese is **22.6**.

---