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Q. 63

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Found in: Page 418

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# A molecular bond can be modeled as a spring between twoatoms that vibrate with simple harmonic motion. FIGURE P15.63shows an SHM approximation for the potential energy of an HClmolecule. Because the chlorine atom is so much more massivethan the hydrogen atom, it is reasonable to assume that the hydrogenatom vibrates back and forth whilethe chlorine atom remains at rest. Use the graph to estimate thevibrational frequency of the HCl molecule.

The vibrational frequency of HCl molecule is

See the step by step solution

## Step 1: Concepts and principles

Elastic Potential energy: The elastic potential energy of a spring-like body of spring constant that has been stretched or compressed a distance x from the undistorted position is:

The frequency of an oscillation in simple harmonic motion is given by

## Step 2:  Given data

Figure P15.63 displays as an approximate SHM for the potential energy of the HCl molecule

The hydrogen atom in Hcl oscillates back and forth while the chlorine atom remains in the experiment

The mass of the hydrogen atom is

The objective is to calculate the vibrational frequency of the Hcl molecule

## Step 3: Solution

As we can see in Fig p 15.63 , the equilibrium length of the bond is

The elastic energy stored in Hcl molecule is

Solve

Equation (3)

## Step 4

Thus, the average value of is

## Step 5

The vibrational frequency of Hcl molecule can be obtained from equation