Final answer:
According to the Maxwell-Boltzmann distribution, less than 50% of molecules have more kinetic energy than the average, exactly 50% more than the median, more than 50% more than the mode, and nearly all have more than the minimum.
Step-by-step explanation:
According to the Maxwell-Boltzmann distribution, the proportion of gas molecules with different kinetic energy levels is described by a skew curve where the following can be determined:
- a) More kinetic energy than average: Less than 50% of molecules will have more kinetic energy than the average, since average (mean) is affected by high-energy outliers.
- b) More kinetic energy than median: Exactly 50% of the molecules will have more kinetic energy than the median, as the median is the middle value by definition.
- c) More kinetic energy than mode: More than 50% of molecules will have more kinetic energy than the mode, which is the most probable energy and is less than the average energy due to the skewness of the distribution.
- d) More kinetic energy than minimum: Essentially all molecules will have more kinetic energy than the minimum, as the minimum energy is zero for a resting molecule (in the absence of quantum effects).
The Maxwell-Boltzmann distribution is a fundamental concept in statistical mechanics that applies to the distribution of molecular speeds in an ideal gas. This distribution is determined by the temperature of the gas, where increasing temperature will result in a higher most probable speed and a broader distribution of speeds.