Among following species which of them have maximum `Z_(eff)`

Options

A. `Sn`
B. `Sn^(4+)`
C. `In`
D. `In^(+)`

Answer

To determine which species has the maximum effective nuclear charge (Z_eff), we will follow these steps:

### Step 1: Understand the concept of Z_eff
Z_eff (effective nuclear charge) is the net positive charge experienced by an electron in a multi-electron atom. It can be calculated using the formula:
\[ Z_{eff} = \frac{Z}{N} \]
where \( Z \) is the total nuclear charge (atomic number) and \( N \) is the number of electrons.

### Step 2: Analyze the given species
Let's consider the species mentioned in the video: Sn, Sn⁴⁺, In, and In⁺.

### Step 3: Calculate Z_eff for each species
1. **For Sn (Tin)**
- Atomic number (Z) = 50
- Number of electrons (N) = 50
- Calculation:
\[ Z_{eff} = \frac{50}{50} = 1.00 \]

2. **For Sn⁴⁺ (Tin with a +4 charge)**
- Atomic number (Z) = 50
- Number of electrons (N) = 50 - 4 = 46
- Calculation:
\[ Z_{eff} = \frac{50}{46} \approx 1.087 \]

3. **For In (Indium)**
- Atomic number (Z) = 49
- Number of electrons (N) = 49
- Calculation:
\[ Z_{eff} = \frac{49}{49} = 1.00 \]

4. **For In⁺ (Indium with a +1 charge)**
- Atomic number (Z) = 49
- Number of electrons (N) = 49 - 1 = 48
- Calculation:
\[ Z_{eff} = \frac{49}{48} \approx 1.021 \]

### Step 4: Compare the Z_eff values
- Sn: Z_eff = 1.00
- Sn⁴⁺: Z_eff ≈ 1.087
- In: Z_eff = 1.00
- In⁺: Z_eff ≈ 1.021

### Step 5: Conclusion
The species with the maximum Z_eff is Sn⁴⁺, with a value of approximately 1.087.

### Final Answer
The species with the maximum Z_eff is **Sn⁴⁺**.

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