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  • The root mean square (rms) speed of oxygen molecules &nb

The root mean square (rms) speed of oxygen molecules \left(\mathrm{O}_{2}\right) of a certain temperature $T$ (degree absolute) is v. If the temperature is doubled and oxygen gas dissociates into atomic oxygen. Find out the rms speed in atomic form -

Option: 1

6 \mathrm{~V}


Option: 2

3 \mathrm{~V}


Option: 3

2 \mathrm{~V}


Option: 4

8 \mathrm{~V}


Answers (1)

best_answer

Root mean square speed V=\sqrt{\frac{3 R T}{M \omega}}

when the temperature is doubled, the new temperature T^{1}=2 T and oxygen \left(\mathrm{O}_{2}\right) dissociates in atomic oxygen, then molecular weight,

\begin{aligned} M_{\omega}^{\prime} & =\frac{M_{\omega}}{2} \\ V^{\prime} & =\sqrt{\frac{3 R T}{M_{\omega}}}=\sqrt{\frac{3 R(2 T)}{(M \omega / 2)}}=\sqrt{4\left(\frac{3 R T}{M \omega}\right)} \\ \Rightarrow V^{\prime}=2 \mathrm{~V} & =\sqrt[2]{\frac{3 R T}{M_{\omega}}} \end{aligned}

Posted by

seema garhwal

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