23P1Q13

13 B

Mass of each molecule, $\displaystyle \begin{aligned} & m=(2.9\times {{10}^{-2}})\div {{N}_{A}} \\ & =(2.9\times {{10}^{-2}})\div (6.02\times {{10}^{23}}) \\ & =4.817\times {{10}^{-26}}\text{ kg} \end{aligned}$

Maximum speed of air molecule, $\displaystyle \begin{aligned} & {{v}_{\max }}=\omega {{x}_{0}} \\ & =(\frac{2\pi }{0.003})(2\times {{10}^{-6}}) \\ & =4.189\times {{10}^{-3}}\text{ m }{{\text{s}}^{-1}} \end{aligned}$

Maximum KE of air molecule, $\displaystyle \begin{aligned} & K{{E}_{\max }}=\frac{1}{2}(4.817\times {{10}^{-26}}){{(4.189\times {{10}^{-3}})}^{2}} \\ & =4.23\times {{10}^{-31}}\text{ J} \end{aligned}$

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