The fundamental frequency of CO is 6.42 *1013 Hz.If the atomic masses are 12 u and 16 u (1 u = 1.66 *10-27 kg), find the force constant (in N/m) for the diatomic molecule.
A)970
B)1530
C)1850
D)480
E)47

Question

Quizplus · Accepted Answer

The force constant of a diatomic molecule can be determined using the equation:
ν = (1/2π) √(k/μ)
where ν is the fundamental frequency, k is the force constant, and μ is the reduced mass of the molecule.
Using the given value of the fundamental frequency and the atomic masses of CO, we can calculate the reduced mass:
μ = (m1 * m2) / (m1 + m2) = (12 u * 16 u) / (12 u + 16 u) = 6.857 u
Converting u to kg:
μ = 1.137 * 10^-26 kg
Substituting the given values into the equation and solving for k:
6.42 * 10^13 Hz = (1/2π) √(k/(1.137 * 10^-26 kg))
k = (6.42 * 10^13 Hz)^2 * 2π * 1.137 * 10^-26 kg = 1.85 * 10^3 N/m
Therefore, the correct answer is choice C.

The Fundamental Frequency of CO Is 6