Final answer:
The question requires determining the gas temperature for a specific difference in molecular speeds, but lacks enough information to solve part (a). The relation between temperature and molecular speeds in a gas is given by kinetic theory formulas, but the most probable speed is not provided.
Step-by-step explanation:
The question asks to determine the gas temperature at which the root mean square velocity (Urms) of hydrogen molecules exceeds their most probable velocity by Δv=400m/s. The key concept here is the relationship between the rms speed of gas molecules, the temperature of the gas, and the molar mass of the gas, which can be described by the formula derived from the kinetic theory of gases: Urms = √(3kBT/M), where kB is the Boltzmann constant, T is the temperature in kelvins, and M is the molar mass of the gas in kilograms per mole.
For part (a), we are not provided with enough information to directly compute the temperature, because the most probable speed (vp) has not been given or a relationship between Urms and Δv that includes temperature. Generally, the most probable speed is calculated using the formula vp = √(2kBT/M). However, without additional information or context, we cannot answer part (a) of the question.
For part (b), if it were asking about atomic hydrogen near the Sun, one would use the given temperature to find the Urms using the same kinetic theory formula albeit for single hydrogen atoms (H) with a different mass.