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?

We need to find the effect on the root mean square (rms) velocity of oxygen molecules when the temperature is doubled and the oxygen molecule dissociates into atomic oxygen.

Write the formula for rms velocity.

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

where $$M$$ is the molar mass and $$T$$ is the temperature.

Calculate the initial rms velocity for O$$_2$$.

For molecular oxygen: $$M_{O_2} = 32$$ g/mol, temperature = $$T$$

$$v_1 = \sqrt{\frac{3RT}{32}}$$

Calculate the new rms velocity for atomic oxygen at doubled temperature.

For atomic oxygen: $$M_O = 16$$ g/mol, temperature = $$2T$$

$$v_2 = \sqrt{\frac{3R(2T)}{16}} = \sqrt{\frac{6RT}{16}}$$

Find the ratio of velocities.

$$\frac{v_2}{v_1} = \sqrt{\frac{6RT/16}{3RT/32}} = \sqrt{\frac{6RT \times 32}{16 \times 3RT}} = \sqrt{\frac{192}{48}} = \sqrt{4} = 2$$

The velocity of atomic oxygen is doubled compared to the original velocity of molecular oxygen.

The correct answer is Option B.