The root mean square speed ($v_{rms}$) of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, implying $v_{rms} \propto \sqrt{\frac{T}{M}}$ .

Given:

1. Hydrogen ($H_2$): $T_1 = 300 \text{ K}$, $v_1 = 1930 \text{ m/s}$. Molar mass $M_1 = 2 \text{ g/mol}$ .
2. Oxygen ($O_2$): $T_2 = 900 \text{ K}$. Molar mass $M_2 = 32 \text{ g/mol}$ .

Calculation: $\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{T_2}{T_1} \times \frac{M_1}{M_2}}$ $\frac{v_{O_2}}{1930} = \sqrt{\frac{900}{300} \times \frac{2}{32}} = \sqrt{3 \times \frac{1}{16}} = \frac{\sqrt{3}}{4}$ $v_{O_2} = 1930 \times \frac{1.732}{4} \approx 836 \text{ m/s}$.