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  4. At what temperature most probable speed of O2 molecules have the same value of root mean square speed of O2 molecules at 300 K ?

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Q. At what temperature most probable speed of $O_{2}$ molecules have the same value of root mean square speed of $O_{2}$ molecules at $300\, K$ ?

States of Matter

Solution:

$\frac{U_{Mp}}{U_{rms}}=\sqrt{\frac{\frac{2RT_{1}}{M}}{\frac{3RT_{2}}{M}}}$
$=\sqrt{\frac{2T_{1}}{3T_{2}}}$
$\Rightarrow \frac{2}{3} \frac{T_{1}}{T_{2}}=1$
$T_{1}=\frac{3}{2}\times300=450\,K$