In two different polar molecules, the ionic charge is 9.6 x 10-10 e.s.u and 3.2 x 10-19 coulombs respectively. If inter ionic distance in both the molecules is 1 A unit, then the dipole moment are respectively

Options

A. `4.8D, 4.8D`
B. `1D, 4.8D`
C. 9.6D, 9.6D
D. 3.33D, 4.8D

Answer

To solve the problem of finding the dipole moments of two different polar molecules given their ionic charges and inter-ionic distances, 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 charge,
- \( d \) is the distance between the charges.

### Step 2: Convert the Given Charges
We have two charges:
1. \( q_1 = 9.6 \times 10^{-10} \) e.s.u.
2. \( q_2 = 3.2 \times 10^{-19} \) coulombs.

For the first charge, we can use it directly in e.s.u. For the second charge, we need to convert coulombs to e.s.u. using the conversion factor:
\[ 1 \text{ coulomb} = 3 \times 10^9 \text{ e.s.u.} \]
Thus, we convert \( q_2 \):
\[ q_2 = 3.2 \times 10^{-19} \text{ coulombs} \times 3 \times 10^9 \text{ e.s.u.} = 9.6 \times 10^{-10} \text{ e.s.u.} \]

### Step 3: Determine the Inter-Ionic Distance
The inter-ionic distance is given as:
\[ d = 1 \text{ Å} = 1 \times 10^{-8} \text{ cm} \]

### Step 4: Calculate the Dipole Moment for Each Charge
1. **For the first charge**:
\[ \mu_1 = q_1 \times d = (9.6 \times 10^{-10} \text{ e.s.u.}) \times (1 \times 10^{-8} \text{ cm}) = 9.6 \times 10^{-18} \text{ e.s.u. cm} \]

2. **For the second charge** (which we found to be the same as the first):
\[ \mu_2 = q_2 \times d = (9.6 \times 10^{-10} \text{ e.s.u.}) \times (1 \times 10^{-8} \text{ cm}) = 9.6 \times 10^{-18} \text{ e.s.u. cm} \]

### Step 5: Final Results
Both dipole moments are the same:
- \( \mu_1 = 9.6 \times 10^{-18} \text{ e.s.u. cm} \)
- \( \mu_2 = 9.6 \times 10^{-18} \text{ e.s.u. cm} \)

### Conclusion
The dipole moments of the two polar molecules are:
- **Dipole Moment 1**: \( 9.6 \times 10^{-18} \text{ e.s.u. cm} \)
- **Dipole Moment 2**: \( 9.6 \times 10^{-18} \text{ e.s.u. cm} \)