Diatomic molecules such as H₂ and F₂ undergo simple harmonic motion with frequencies that obey Hooke's Law, with an effective mass equal to half the atomic mass. If the mass of a hydrogen atom is 1.627 × 10⁻²⁷ kg and the mass of a fluorine atom is 3.17 × 10⁻²⁶ kg, what is the approximate ratio of the oscillation frequency of H₂ to that of F₂, assuming the bond strengths are the same? A) 360 B) 19 C) 38 D) 4.4 E) 9.5

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Quizplus · Accepted Answer

The oscillation frequency is inversely proportional to the square root of the mass. Therefore, the ratio of the oscillation frequency of H₂ to that of F₂ is:$$\frac{f_{H_2}}{f_{F_2}}=\sqrt{\frac{m_{F_2}}{m_{H_2}}}=\sqrt{\frac{3.17 imes10^{-26} ext{ kg}}{1.627 imes10^{-27} ext{ kg}}}=\sqrt{19}\approx4.4$$

Diatomic Molecules Such as H2 and F2 Undergo Simple Harmonic

Diatomic Molecules Such as H₂ and F₂ Undergo Simple Harmonic