Diatomic molecule has a dipole moment of `1.2D` If its bond `1.0 Å` what fraction of an electronic charge exists on each atom ? .

Options

A. `0.50`
B. `1.2 xx 10^(-10)`
C. `0.25`
D. `1.2`

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Given Information
We have a diatomic molecule with:
- Dipole moment (μ) = 1.2 Debye
- Bond length (D) = 1.0 Å

### Step 2: Convert Units
1. **Convert Dipole Moment from Debye to Electrostatic Units (ESU)**:
- 1 Debye = \( 3.336 \times 10^{-29} \) C·m
- Therefore, \( 1.2 \, \text{D} = 1.2 \times 3.336 \times 10^{-29} \, \text{C·m} \)
- Calculate:
\[ \mu = 1.2 \times 3.336 \times 10^{-29} \approx 4.0032 \times 10^{-29} \, \text{C·m} \]

2. **Convert Bond Length from Ångström to Electrostatic Units**:
- 1 Å = \( 10^{-10} \) m
- Therefore, \( 1.0 \, \text{Å} = 1.0 \times 10^{-10} \, \text{m} = 1.0 \times 10^{-8} \, \text{cm} \)

### Step 3: Use the Dipole Moment Formula
The dipole moment (μ) is related to the charge (δ) and the distance (D) by the formula:
\[ \mu = \delta \cdot D \]
Rearranging this gives:
\[ \delta = \frac{\mu}{D} \]

### Step 4: Substitute the Values
Substituting the values we have:
\[ \delta = \frac{4.0032 \times 10^{-29} \, \text{C·m}}{1.0 \times 10^{-10} \, \text{m}} \]
Calculating this gives:
\[ \delta = 4.0032 \times 10^{-19} \, \text{C} \]

### Step 5: Find the Fraction of Electronic Charge
The charge of an electron (e) is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]
To find the fraction of the electronic charge on each atom:
\[ \text{Fraction} = \frac{\delta}{e} = \frac{4.0032 \times 10^{-19} \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \]
Calculating this gives:
\[ \text{Fraction} \approx 2.502 \]

### Conclusion
The fraction of an electronic charge that exists on each atom is approximately **0.25** or **25%** of the electronic charge.