The electric dipole moment of an electron and a proton 4.3 nm apart, is

Options

A. `6.8 xx 10^(-28) C - m`
B. `2.56 xx 10^(-29) C^(2)//m`
C. `3.72 xx 10^(-14) C//m`
D. `11 xx 10^(-46) C^(2)//m`

Answer

To find the electric dipole moment of an electron and a proton that are 4.3 nm apart, we can follow these steps:

### Step 1: Understand the concept of electric dipole moment
The electric dipole moment (\( p \)) is defined as the product of the charge (\( Q \)) and the distance (\( d \)) between the charges. For a dipole consisting of an electron and a proton, we have:
\[ p = Q \cdot d \]

### Step 2: Identify the charges involved
The charge of an electron is \( -e \) and the charge of a proton is \( +e \). The magnitude of the charge \( e \) is approximately:
\[ e = 1.6 \times 10^{-19} \text{ C} \]

### Step 3: Convert the distance from nanometers to meters
The distance \( d \) between the electron and proton is given as 4.3 nm. We need to convert this to meters:
\[ d = 4.3 \text{ nm} = 4.3 \times 10^{-9} \text{ m} \]

### Step 4: Substitute the values into the dipole moment formula
Now we can substitute the values of \( Q \) and \( d \) into the formula for the electric dipole moment:
\[ p = e \cdot d = (1.6 \times 10^{-19} \text{ C}) \cdot (4.3 \times 10^{-9} \text{ m}) \]

### Step 5: Perform the multiplication
Calculating the product:
\[ p = 1.6 \times 4.3 \times 10^{-19} \times 10^{-9} \]
Calculating \( 1.6 \times 4.3 \):
\[ 1.6 \times 4.3 \approx 6.88 \]
Thus:
\[ p \approx 6.88 \times 10^{-28} \text{ C m} \]

### Step 6: Round off the result
Rounding off to two significant figures, we have:
\[ p \approx 6.9 \times 10^{-28} \text{ C m} \]

### Final Answer
The electric dipole moment of the electron and proton 4.3 nm apart is approximately:
\[ p \approx 6.9 \times 10^{-28} \text{ C m} \]