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Q. 61

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 656

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Short Answer

The ozone molecule has a permanent dipole moment of 1. Although the molecule is very slightly bent— which is why it has a dipole moment—it can be modeled as a uniform rod of length with the dipole moment perpendicular to the axis of the rod. Suppose an ozone molecule is in a uniform electric field. In equilibrium, the dipole moment is aligned with the electric field. But if the molecule is rotated by a small angle and released, it will oscillate back and forth in simple harmonic motion. What is the frequency of oscillation?

The frequency of oscillation is

See the step by step solution

Step by Step Solution

Step 1 : Given information and formula used

Given :

The ozone molecule has a dipole moment : .

It can be modeled as a uniform rod of length :

Ozone molecule is in an electric field :

In equilibrium, the dipole moment is aligned with the electric field.

Theory used :

The motion of the molecule is periodic, recurring in a sinusoidal pattern with a constant amplitude .

A basic harmonic oscillator's motion is defined by its period , which is the time it takes for a single oscillation, or its frequency .

The phase, which controls the starting point on the sine wave, also influences the position at a given time . The size of the mass and the force constant determine the period and frequency, whereas the starting location and velocity dictate the amplitude and phase.

A dipole is torqued by the electric field . The dipoles are aligned by the torque.

Step 2 : Calculating the frequency of oscillation 

Period is :

Oscillation frequency :

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