Final answer:
The sample of gas with the greatest root mean square speed is Neon (Ne) at 310 K because it is the lighter gas and at a higher temperature compared to the other samples.
Step-by-step explanation:
The root mean square speed of gas molecules is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass. Given the gases Neon (Ne) and Xenon (Xe) at different temperatures, we apply the principle that higher temperatures result in higher speeds, and lighter gases (lower molar mass) move faster than heavier gases at the same temperature.
Between Ne at 310 K and Ne at 298 K, sample (a) Ne at 310 K will have a higher root mean square speed due to the higher temperature. Comparing Xe at the same temperatures, Xe at 310 K (d) will have a higher speed than Xe at 298 K (c) for the same reason. However, Ne is lighter than Xe, so between Ne at 310 K and Xe at 310 K, Ne at 310 K (a) will have the greatest root mean square speed.
Therefore, the correct answer is (a) Ne at 310 K.