In a polar molecule , the ionic charge is `4.8 xx 10^(-10)` esu. If the interatomic distance is `1 Å` unit, then the dipole moment is

Options

A. `41.8` debey
B. `4.18` debye
C. `4.8` debye
D. `0.48` debye

Answer

To find the dipole moment of a polar molecule given the ionic charge and interatomic distance, we can follow these steps:

### Step 1: Understand the formula for dipole moment
The dipole moment (μ) is calculated using the formula:
\[ \mu = q \times d \]
where:
- \( \mu \) is the dipole moment,
- \( q \) is the magnitude of the ionic charge,
- \( d \) is the distance between the charges.

### Step 2: Identify the given values
From the question, we have:
- Ionic charge \( q = 4.8 \times 10^{-10} \) esu,
- Interatomic distance \( d = 1 \) Å.

### Step 3: Convert the distance from Ångstroms to centimeters
1 Ångstrom (Å) is equal to \( 10^{-8} \) centimeters. Therefore:
\[ d = 1 \, \text{Å} = 1 \times 10^{-8} \, \text{cm} \]

### Step 4: Substitute the values into the dipole moment formula
Now we can substitute the values of \( q \) and \( d \) into the dipole moment formula:
\[ \mu = (4.8 \times 10^{-10} \, \text{esu}) \times (1 \times 10^{-8} \, \text{cm}) \]

### Step 5: Perform the multiplication
Calculating the product:
\[ \mu = 4.8 \times 10^{-10} \times 10^{-8} = 4.8 \times 10^{-18} \, \text{esu cm} \]

### Step 6: Convert the dipole moment to Debye
1 Debye (D) is defined as \( 10^{-18} \, \text{esu cm} \). Therefore, we can convert the dipole moment to Debye:
\[ \mu = 4.8 \, \text{D} \]

### Conclusion
The dipole moment of the polar molecule is \( 4.8 \, \text{D} \).

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