# Step-by-Step Solution ## 1. **Given Data** - Dipole moment of ammonia, \( p = 1.47 \) D - \( 1 \) D (debye) \( = 3.34 \times 10^{-30} \) C·m - Distance from dipole, \( r = 63.2 \) nm \( = 63.2 \times 10^{-9} \) m - We are asked for the electric potential \( V \) **along the axis** of the dipole. - Set \( V = \) at infinity. --- ## 2. **Convert Dipole Moment to SI Units** \[ p = 1.47~ \text{D} = 1.47 \times 3.34 \times 10^{-30}~\text{C·m} \] \[ p = 4.9098 \times 10^{-30}~\text{C·m} \] --- ## 3. **Formula for Dipole Potential (on Axis)** The potential at a point distance \( r \) **on the axis** of an ideal dipole is: \[ V = \frac{1}{4\pi\varepsilon_} \frac{2p}{r^2} \] Where: - \( \varepsilon_ = 8.854 \times 10^{-12}~\text{C}^2/\text{N·m}^2 \) --- ## 4. **Plug in the Values** ### Compute \( \frac{1}{4\pi\varepsilon_} \): \[ \frac{1}{4\pi\varepsilon_} = 9 \times 10^9~\text{N·m}^2/\text{C}^2 \] ### Plug in all values: \[ V = 9 \times 10^9 \times \frac{2 \times 4.9098 \times 10^{-30}}{(63.2 \times 10^{-9})^2} \] --- ## 5. **Calculate the Denominator** \[ (63.2 \times 10^{-9})^2 = (63.2)^2 \times (10^{-9})^2 = 3994.24 \times 10^{-18} = 3.99424 \times 10^{-15} \] --- ## 6. **Calculate the Numerator** \[ 2 \times 4.9098 \times 10^{-30} = 9.8196 \times 10^{-30} \] --- ## 7. **Calculate the Fraction** \[ \frac{9.8196 \times 10^{-30}}{3.99424 \times 10^{-15}} = \frac{9.8196}{3.99424} \times 10^{-30 + 15} \] \[ = 2.459 \times 10^{-15} \] --- ## 8. **Multiply by \( 9 \times 10^9 \) to get \( V \)** \[ V = 9 \times 10^9 \times 2.459 \times 10^{-15} \] \[ = 22.131 \times 10^{-6} \] \[ = 2.21 \times 10^{-5}~\text{V} \] --- ## 9. **Final Answer** \[ \boxed{V = 2.2 \times 10^{-5}~\text{V}} \] at a point 63.2 nm away along the axis of the ammonia dipole. --- ### **Summary Table** | Quantity | Value | |------------------|-------------------------------| | Dipole moment | \( 1.47~\text{D} = 4.91 \times 10^{-30}~\text{C·m} \) | | Distance | \( 63.2~\text{nm} = 6.32 \times 10^{-8}~\text{m} \) | | Potential \( V \)| \( 2.2 \times 10^{-5}~\text{V} \) |