A diatomic molecule has a dipole moment of 1.2 D. If its bond length is equal to `10^(-10)` m then the fraction of an electronic charge on each atom will be

Options

A. `45%`
B. `55%`
C. `75%`
D. `25%`

Answer

To solve the problem, we need to calculate the fraction of an electronic charge on each atom of a diatomic molecule given its dipole moment and bond length.

### Step-by-Step Solution:

1. **Understand the Dipole Moment Formula**:
The dipole moment (μ) of a diatomic molecule is given by the formula:
\[ \mu = q \cdot d \]
where \( q \) is the charge on each atom, and \( d \) is the bond length.

2. **Convert Dipole Moment from Debye to ESU**:
The dipole moment is given as 1.2 D (Debye). We need to convert this to electrostatic units (ESU):
\[ 1 \text{ D} = 3.33 \times 10^{-10} \text{ ESU cm} \]
Therefore,
\[ 1.2 \text{ D} = 1.2 \times 3.33 \times 10^{-10} \text{ ESU cm} = 4.0 \times 10^{-10} \text{ ESU cm} \]

3. **Convert Bond Length to Centimeters**:
The bond length is given as \( 10^{-10} \) m. We need to convert this to centimeters:
\[ 10^{-10} \text{ m} = 10^{-10} \times 100 \text{ cm} = 10^{-8} \text{ cm} \]

4. **Substitute Values into the Dipole Moment Formula**:
Now we can substitute the values into the dipole moment formula:
\[ 4.0 \times 10^{-10} = q \cdot 10^{-8} \]

5. **Solve for Charge (q)**:
Rearranging the equation to solve for \( q \):
\[ q = \frac{4.0 \times 10^{-10}}{10^{-8}} = 4.0 \times 10^{-2} \text{ ESU} \]

6. **Convert Charge from ESU to Coulombs**:
We know that:
\[ 1 \text{ ESU} = 3.33 \times 10^{-10} \text{ C} \]
Therefore, converting \( q \) to coulombs:
\[ q = 4.0 \times 10^{-2} \text{ ESU} \times 3.33 \times 10^{-10} \text{ C/ESU} = 1.33 \times 10^{-11} \text{ C} \]

7. **Find the Fraction of Electronic Charge**:
The charge of an electron is approximately \( 1.6 \times 10^{-19} \text{ C} \). To find the fraction of the electronic charge on each atom:
\[ \text{Fraction} = \frac{q}{\text{Charge of an electron}} = \frac{1.33 \times 10^{-11}}{1.6 \times 10^{-19}} = 0.083125 \]

8. **Convert Fraction to Percentage**:
To express this fraction as a percentage:
\[ \text{Percentage} = 0.083125 \times 100 = 8.3125\% \]

9. **Final Answer**:
The fraction of the electronic charge on each atom is approximately \( 8.31\% \).