(II) The HCl molecule has a dipole moment of about 3.4 x 10⁻³⁰ C•m. The two atoms are separated by about 1.0 x 10⁻¹⁰.m
(a) What is the net charge on each atom?


(b) Is this equal to an integral multiple of e? If not, explain.
(c) What maximum torque would this dipole experience in a 2.5 x 10⁴ N/C electric field?
(d) How much energy would be needed to rotate one molecule 45° from its equilibrium position of lowest potential energy?

Verified step by step guidance

1. (a) To find the net charge on each atom, use the formula for the dipole moment, $p=q\times d$, where $p$ is the dipole moment, $q$ is the magnitude of the charge on each atom, and $d$ is the separation between the charges. Rearrange the formula to solve for $q$: $q=\frac{p}{d}$.
2. (b) To determine if the charge is an integral multiple of the elementary charge $e$, calculate $q$ from step (a) and divide it by $e$ ($e=1.6\times {10}^{-19}C$). Check if the result is an integer.
3. (c) To find the maximum torque experienced by the dipole in an electric field, use the formula $\tau =p\times E$, where $\tau$ is the torque, $p$ is the dipole moment, and $E$ is the electric field strength. The maximum torque occurs when the angle between $p$ and $E$ is 90 degrees, making $\tau =pE$.
4. (d) To calculate the energy needed to rotate the molecule by 45°, use the formula for the potential energy of a dipole in an electric field, $U=-p\cdot E\cdot \cos (\theta )$. Calculate the change in potential energy as $\mathrm{\Delta }U=U_{\text{final}}-U_{\text{initial}}$, where ${\theta }_{\text{initial}}$ is the angle of lowest potential energy (typically 0 degrees) and ${\theta }_{\text{final}}$ is 45 degrees.

Key Concepts

Dipole Moment

The dipole moment is a vector quantity that measures the separation of positive and negative charges in a system. It is defined as the product of the charge and the distance between the charges. In the case of HCl, the dipole moment indicates the polarity of the molecule, which affects its behavior in electric fields.

Electric Field

An electric field is a region around a charged particle where other charged particles experience a force. It is quantified in newtons per coulomb (N/C) and influences the motion of charged particles. The strength of the electric field affects the torque experienced by a dipole, as it interacts with the dipole moment.

Torque on a Dipole

Torque on a dipole in an electric field is the measure of the rotational force acting on the dipole due to the field. It is calculated using the formula τ = pE sin(θ), where τ is the torque, p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field. This concept is crucial for understanding how dipoles align with electric fields.