Calculation of Force Constant for CO Molecule

Study Notes

Calculation of Force constant for CO

The problem asks to calculate the force constant of a CO molecule using the spacing between its vibrational energy levels.
The spacing is given as 8.44 x 10^-2 eV, which needs to be converted to Joules using the conversion factor 1 eV = 1.6 x 10^-19 J.
The reduced mass of CO is provided as 1.14 x 10^-26 kg along with Planck's constant (6.626 x 10^-34 J s).
To solve for the force constant, we'll need a formula that connects vibrational energy levels to reduced mass, Planck's constant, and force constant.
The formula used is likely the equation for the energy levels of a harmonic oscillator: E(n) = (n + 1/2) * h * f, where E(n) is the energy of the nth level, h is Planck's constant, and f is the vibrational frequency.
The spacing between energy levels is then given by: ΔE = h * f
The vibrational frequency is related to the force constant (k) and reduced mass (μ) by the formula: f = 1/(2π) * √(k/μ).
Solving these equations to find the force constant (k) requires combining the expressions for ΔE and f.
Using the provided values for the energy spacing, reduced mass, and constants, we can calculate the force constant.
The answer choices (a) 1.87 N/m, (b) 18.7 N/m, (c) 187 N/m, and (d) 1870 N/m provide the possible values for the force constant.
The correct answer will depend on the specific calculations and the choice of units used.

Description

This quiz focuses on calculating the force constant of the carbon monoxide (CO) molecule using its vibrational energy levels. You'll apply concepts such as reduced mass, Planck's constant, and the harmonic oscillator model to derive the force constant from the given energy spacing. Test your understanding of vibrational mechanics and energy levels with this practical application.