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AP EAMCET · PHYSICS · Kinetic Theory of Gases

The rms speed of oxygen molecule at a certain temperature is \(600 \mathrm{~ms}^{-1}\). If the temperature is doubled and oxygen molecule dissociates into atomic oxygen atoms, the new rms speed is

  1. A \(120 \mathrm{~ms}^{-1}\)
  2. B \(150 \mathrm{~ms}^{-1}\)
  3. C \(1200 \mathrm{~ms}^{-1}\)
  4. D \(600 \mathrm{~ms}^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(1200 \mathrm{~ms}^{-1}\)

Step-by-step Solution

Detailed explanation

\(v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}\) Given, at temperature \(T_1\), \(v_{ rms }=600=\sqrt{\frac{3 R T_1}{M}}\) ...(i) At temperature, \(T_2=2 \pi T_1\), due to dissociation \(v_{ rms }=v=\sqrt{\frac{3 R\left(2 T_1\right)}{(M / 2)}}\) ...(ii) Dividing Eq. (i) by Eq. (ii),…
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