Calculation of Force Constant for CO Molecule

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.