What is the Harmonic Vibrational Frequency of a 39^K 35^Cl Molecule?

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Homework Help Overview

The discussion revolves around determining the harmonic vibrational frequency of a 39^K 35^Cl molecule, which consists of potassium and chlorine ions. The problem involves understanding the forces acting between these ions, specifically the electrostatic attraction and the short-range repulsive forces, and how they relate to the harmonic motion of the molecule.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss deriving an expression for the force constant using Hooke’s law and consider equating the Coulomb force to the spring-like repulsive force to find the necessary parameters for calculating the vibrational frequency.

Discussion Status

Some participants have offered insights into the relationship between the forces acting on the ions and the application of Hooke's law. There is an ongoing exploration of how to set up the equations needed to derive the frequency, with no explicit consensus reached yet.

Contextual Notes

Participants are working under the assumption that the electrostatic forces can be modeled appropriately with Hooke's law and are considering the equilibrium distance provided in the problem. There may be constraints related to the specific details of the forces involved that are not fully addressed.

Ajs51
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1. A molecule of 39^K 35^Cl consists of two ions,39^K+ and 35^Cl−,which are attracted to each other by electrostatic forces. The short-range repulsive force results in an interatomic distance of 2.7 ˚A at equilibrium. Considering only the electrostatic attraction, derive an expression for the force constant using Hooke’s law.Hence, determine the harmonic vibrational frequency of the 39^K 35^Cl molecule in wavenumbers.



3. I just can't seem to do this any help would be appreciated
 
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There is one positive charge on the potassium and one negative charge on the chlorine. The attractive force is from these two opposite charges. It sounds to me like you are supposed to treat the repulsive force as being spring-like. You also know the distance between the atoms when the forces cancel each other out exactly, so that should give you all of the information that you need. Hopefully that points you in the right direction.
 
Oh that makes sense..would it make sense to set the Coulomb force, equal to the hooke law...solve to find k...then use k to find w (angular frequency) ?
 
Also thanks for the help!
 

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