Calculate the screening constant of alkali metals for valenvy electrons.

Explanation

To calculate the screening constant (σ) for alkali metals, we will use the formula:

\[ \sigma = 0.35 \times n + 0.85 \times (n-1) + 1 \times \text{(inner shell electrons)} \]

Where:
- \( n \) is the number of electrons in the outermost shell (nth shell).
- \( n-1 \) is the number of electrons in the shell just below the outermost shell.
- Inner shell electrons are all the electrons in shells below the n-1 shell.

Let’s calculate the screening constant for each alkali metal step by step.

### Step 1: Calculate σ for Lithium (Li)
1. **Electron Configuration**: \( 1s^2 2s^1 \)
- n (outer shell, 2s) = 1 electron
- n-1 (inner shell, 1s) = 2 electrons
- Inner shell = 0 (no other shells below 1s)

2. **Calculation**:
\[ \sigma = 0.35 \times 1 + 0.85 \times 2 + 1 \times 0 = 0.35 + 1.7 + 0 = 2.05 \]

### Step 2: Calculate σ for Sodium (Na)
1. **Electron Configuration**: \( 1s^2 2s^2 2p^6 3s^1 \)
- n (outer shell, 3s) = 1 electron
- n-1 (inner shell, 2s and 2p) = 8 electrons
- Inner shell = 2 electrons (1s)

2. **Calculation**:
\[ \sigma = 0.35 \times 1 + 0.85 \times 8 + 1 \times 2 = 0.35 + 6.8 + 2 = 9.15 \]

### Step 3: Calculate σ for Potassium (K)
1. **Electron Configuration**: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 \)
- n (outer shell, 4s) = 1 electron
- n-1 (inner shell, 3s and 3p) = 8 electrons
- Inner shell = 10 electrons (1s, 2s, 2p)

2. **Calculation**:
\[ \sigma = 0.35 \times 1 + 0.85 \times 8 + 1 \times 10 = 0.35 + 6.8 + 10 = 17.15 \]

### Step 4: Calculate σ for Rubidium (Rb)
1. **Electron Configuration**: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 4p^6 5s^1 \)
- n (outer shell, 5s) = 1 electron
- n-1 (inner shell, 4s, 4p) = 18 electrons
- Inner shell = 28 electrons (1s, 2s, 2p, 3s, 3p, 3d)

2. **Calculation**:
\[ \sigma = 0.35 \times 1 + 0.85 \times 18 + 1 \times 28 = 0.35 + 15.3 + 28 = 43.65 \]

### Step 5: Calculate σ for Cesium (Cs)
1. **Electron Configuration**: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 4p^6 4d^{10} 5s^2 5p^6 6s^1 \)
- n (outer shell, 6s) = 1 electron
- n-1 (inner shell, 5s, 5p) = 46 electrons
- Inner shell = 46 electrons (1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p)

2. **Calculation**:
\[ \sigma = 0.35 \times 1 + 0.85 \times 46 + 1 \times 46 = 0.35 + 39.1 + 46 = 85.45 \]

### Summary of Screening Constants for Alkali Metals
- Lithium (Li): σ = 2.05
- Sodium (Na): σ = 9.15
- Potassium (K): σ = 17.15
- Rubidium (Rb): σ = 43.65
- Cesium (Cs): σ = 85.45