Q69 / 90 · JEE Main 2022 (28 Jun Shift 2) · Physics

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?

A
The velocity of atomic oxygen remains same
Correct answer
B
The velocity of atomic oxygen doubles
C
The velocity of atomic oxygen becomes half
D
The velocity of atomic oxygen becomes four times

Solution

The RMS velocity of a gas is given by, $v_{R M S} = \sqrt{\frac{3 R T}{M}}$

When $O_{2}$ dissociates into $O$ its molecular mass becomes $\frac{M}{2}$ . Therefore,

Ratio of RMS speed, $\frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}} \times \frac{M_{2}}{M_{1}}}$ $\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{T}{2 T} \times \frac{M / 2}{M}}$ $\Rightarrow \frac{v_{2}}{v_{1}} = 2$

Hence, the correct answer is option: 'B'.

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