Diatomic molecules such as H₂ and O₂ undergo simple harmonic motion with frequencies that obey Hooke's Law with the effective mass being half the atomic mass.If the mass of a hydrogen atom is 1.627 $\times$ 10^-27 kg and that of fluorine is 3.17 $\times$ 10^-26 kg,what is the ratio of oscillation frequencies of H₂ to that of F₂,assuming that the bond strength between the atoms of hydrogen is the same as that between fluorine atoms? A) 360 B) 19 C) 38 D) 4.4 E) 9.5

Question

Quizplus · Accepted Answer

The ratio of oscillation frequencies is given by:
$$\frac{f_{HS}}{f_{FS}}=\sqrt{\frac{\mu_{FS}}{\mu_{HS}}}$$
where $\mu$ is the reduced mass of the diatomic molecule. Since the effective mass is half the atomic mass, the reduced mass is given by:
$$\mu=\frac{m_1m_2}{m_1+m_2}=\frac{m}{2}$$
where $m$ is the atomic mass. Thus, we have:
$$\frac{\mu_{FS}}{\mu_{HS}}=\frac{m_F/2}{m_H/2}=\frac{3.17	imes10^{-26}/2}{1.627	imes10^{-27}/2}=19.4$$
Taking the square root gives:
$$\frac{f_{HS}}{f_{FS}}=\sqrt{19.4}\approx4.4$$
Therefore, the correct answer is B) 19.

Diatomic Molecules Such as H2 and O2 Undergo Simple Harmonic ×\times×

Diatomic Molecules Such as H₂ and O₂ Undergo Simple Harmonic $\times$