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Q. 63

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 418

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Short Answer

A molecular bond can be modeled as a spring between two

atoms that vibrate with simple harmonic motion. FIGURE P15.63

shows an SHM approximation for the potential energy of an HCl

molecule. Because the chlorine atom is so much more massive

than the hydrogen atom, it is reasonable to assume that the hydrogen

atom vibrates back and forth while

the chlorine atom remains at rest. Use the graph to estimate the

vibrational frequency of the HCl molecule.

The vibrational frequency of HCl molecule is

See the step by step solution

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

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