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  4. The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is: (Atomic masses: He = 4 u, 0 = 16 u) The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at 300 K is: (Atomic masses: He = 4 u, 0 = 16 u)

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Q. The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at $300\, K$ is : (Atomic masses : $He = 4 \,u, 0 = 16 \,u)$ The temperature at which oxygen molecules have the same root mean square speed as helium atoms have at $300\, K$ is : (Atomic masses : $He = 4 \,u, 0 = 16 \,u)$

JEE MainJEE Main 2014States of Matter

Solution:

$\left(U_{rms}\right)_{o_2} =\left(U_{rms}\right)_{He}$

$\Rightarrow \frac{3RTo_{2}}{32}=\frac{3R T_{He}}{4}$

$\Rightarrow T_{o_2} =8\times300=2400 \,K$