At what temperature will the \(\text{rms}\) speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere? 
(Given: Mass of oxygen molecule \((m)= 2.76\times 10^{-26}~\text{kg}\), Boltzmann's constant \(k_B= 1.38\times10^{-23}~\text{J K}^{-1}\))
1. \(2.508\times 10^{4}~\text{K}\)
2. \(8.360\times 10^{4}~\text{K}\)
3. \(5.016\times 10^{4}~\text{K}\)
4. \(1.254\times 10^{4}~\text{K}\)

The molecules of a given mass of gas have rms velocity of 200 ms^-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10⁵ Nm^-2, rms velocity of its molecules in ms^-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√2