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  • Can someone help me with this, 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, O =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, O =16 u)

  • Option 1)

    300 K

     

  • Option 2)

    600 K

  • Option 3)

    1200 K

  • Option 4)

    2400 K

 

Answers (1)

best_answer

As we have learnt,

 

Rms speed of gas molecules -

Vrms=\sqrt{(3RT/M)}

- wherein

M- Molecular Mass , R- Gas Constant , T- Temperature

 

 

Temperature at which O2 moleclues have same vrms as He atoms 

\\*v_{rms} = \sqrt{\frac{3RT}{M}} \\*\\* \sqrt{\frac{3\times R\times T}{32\times 10^{-3}}} = \sqrt{\frac{3\times R\times T}{4\times 10^{-3}}} \\*v_{rms\;O_2} = v_{rms\;He} \\*\\*\frac{3\times R\times T}{32\times 10^{-3}} = \frac{3\times R \times T}{4\times 10^{-3}} \\*\\*\frac{T}{32} = \frac{300}{4} \Rightarrow T = \frac{300\times 32}{4} = 2400k


Option 1)

300 K

 

Option 2)

600 K

Option 3)

1200 K

Option 4)

2400 K

Posted by

SudhirSol

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