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  4. The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is

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Q. The temperature at which oxygen molecules have the same root mean square speed as that of hydrogen molecules at 300 K is

KEAMKEAM 2010Current Electricity

Solution:

$ \sqrt{\frac{3R{{T}_{O}}}{{{M}_{O}}}}=\sqrt{\frac{3R{{T}_{H}}}{{{M}_{H}}}} $
or $ \frac{{{T}_{O}}}{{{M}_{O}}}=\frac{{{T}_{H}}}{{{M}_{H}}} $
or $ \frac{{{T}_{O}}}{32}=\frac{300}{2} $
or $ {{T}_{O}}=16\times 300 $
$ =4800\,K $