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What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

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The velocity of atomic oxygen becomes four times

The velocity of atomic oxygen remains same

The velocity of atomic oxygen doubles

The velocity of atomic oxygen becomes half

answer is B.

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Detailed Solution

$\begin{array}{l} V_{rms} = \sqrt{\frac{3 RT}{M}} \\ T \to 2 T \\ M \to \frac{M}{2} \\ V_{rms} \propto \sqrt{\frac{T}{M}} \end{array}$

$\Rightarrow {(V_{rms})}_{atomic} = {(V_{rms})}_{molecular} \times \sqrt{\frac{2}{1 / 2}} = 2 {(V_{rms})}_{molecular}$

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