The rms speed of oxygen molecule at a certain temperature is $600 \mathrm{~ms}^{-1}$. If the temperature is…

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. $120 \mathrm{~ms}^{-1}$
  2. $150 \mathrm{~ms}^{-1}$
  3. $1200 \mathrm{~ms}^{-1}$
  4. $600 \mathrm{~ms}^{-1}$

Solution

$v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}}$ Given, at temperature $T_1$,
At temperature, $T_2=2 \pi T_1$, due to dissociation
Dividing Eq. (i) by Eq. (ii), we get $\Rightarrow \quad \frac{v}{600}=2 \quad \Rightarrow v=1200 \mathrm{~ms}^{-1}$

Asked in: MHT CET Full Test 7

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