AMU Medical AMU Solved Paper-2000

  • question_answer
    If the root mean square velocity of the molecules of hydrogen at NTP is 1.84 km/s. Calculate the root mean square velocity of oxygen molecule at NTP molecule weight of hydrogen and oxygen are 2 and 32, respectively.

    A)  1.47km/s .                         

    B)  0.94 km/s

    C)  1.84 km/s                          

    D)  0.47 km/s

    Correct Answer: D

    Solution :

                     Root mean square velocity \[({{v}_{rms}})\] is given by \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\]where M is molecular weight, R the gas constant, and T the absolute temperature. Given,   \[{{v}_{H}}=1.84\,\,km/s\],                 \[{{M}_{H}}=2,\,\,\,{{M}_{O}}=32\]                 \[\frac{{{v}_{H}}}{{{v}_{O}}}=\sqrt{\frac{{{M}_{O}}}{{{M}_{H}}}}\] \[\Rightarrow \]               \[\frac{{{v}_{H}}}{{{v}_{O}}}=\sqrt{\frac{32}{2}}=4\] \[\Rightarrow \]               \[{{v}_{O}}=\frac{{{v}_{H}}}{4}\]                 \[=\frac{1.84}{4}=0.47\,\,km/s\]


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