Question

Give that the spacing of the lines in the microwave spectrum of Al24H1 is constant at 12.604 m-1 .calculate the moment of intertia and bond length of the molecule

Answer 1

Answer on question #74689

\begin{array}{l} \Delta B = 12.604 \, \text{m}^{-1} \\ B = \frac{12.604}{\Delta} = 6.302 \, \text{m}^{-1} \\ B = \frac{h}{8\pi^2 I C} \\ I = \text{moment of Inertia} \\ I = \frac{h}{8\pi^2 B C} \\ I = \frac{6.626 \times 10^{-34} \, \text{kg} \, \text{m}^2 \, \text{s}^{-1}}{8 \times (3.14)^2 \times 6.302 \times 2.998 \times 10^8 \, \text{m}^2 \, \text{s}^{-1}} \\ \text{#} \quad I (\text{moment of Inertia}) = 4.44 \times 10^{-45} \, \text{kg} \, \text{m}^2 \\ I = 4\pi^2 \\ \pi = \sqrt{\frac{4.44}{0.99845}} \times 10^{-45} \\ \text{#} \quad \sqrt{\pi = 6.67 \times 10^{-23} \, \text{m}} \\ \end{array} \quad \begin{array}{l} u = \frac{m_{Al} m_H}{m_{Al} + m_H} = \frac{27 \times 24 \times 1}{27 + 24 + 1} \\ u = 99845 \\ \end{array}

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