Question

A neutral ammonia (NH\(_3\)) molecule in its vapour state has an electric dipole moment of magnitude \( 5 \times 10^{-30} \) C·m. How far apart are the molecule's centers of positive and negative charge?

• A. \( 4.125 \times 10^{-12} \) m
• B. \( 3.125 \times 10^{-12} \) m
• C. \( 3.125 \times 10^{-6} \) m
• D. \( 4.125 \times 10^{-6} \) m

Hint:

The separation distance between charges in a dipole is given by \( d = \frac{p}{q} \). - Ensure charge \( q \) is in Coulombs and dipole moment \( p \) in C·m before calculation.

Answer 1

The Correct Option is B

To find the separation distance between the centers of positive and negative charge in an ammonia (NH₃) molecule, we use the definition of the electric dipole moment, which is given by the equation:

\( p = q \times d \)

where:

• p is the electric dipole moment (5 × 10^-30 C·m).
• q is the charge of the electron or proton (approximately 1.6 × 10^-19 C).
• d is the separation distance between the charge centers (the value we need to find).

We rearrange the equation to solve for d:

\( d = \frac{p}{q} \)

Substituting the known values:

\( d = \frac{5 \times 10^{-30}}{1.6 \times 10^{-19}} \)

Calculating the above:

\( d = 3.125 \times 10^{-12} \) m

Thus, the separation distance between the centers of positive and negative charge in the ammonia molecule is \( 3.125 \times 10^{-12} \) m, which corresponds to one of the given options.

Answer 2

To determine the separation distance between the centers of positive and negative charge in the ammonia (NH\(_3\)) molecule, we use the formula for the electric dipole moment, given by:

\( \mu = q \times d \)

where:

• \(\mu\) is the dipole moment, \(5 \times 10^{-30}\) C·m.
• \(q\) is the charge of the electron, approximately \(1.6 \times 10^{-19}\) C.
• \(d\) is the separation distance we need to find.

Rearranging the formula to solve for \(d\), we get:

\( d = \frac{\mu}{q} \)

Substituting the given values:

\( d = \frac{5 \times 10^{-30}}{1.6 \times 10^{-19}} \)

Calculating the value:

\( d \approx 3.125 \times 10^{-12} \) m

Thus, the separation distance between the centers of positive and negative charge in the ammonia molecule is \(3.125 \times 10^{-12}\) m.