Final answer:
The mean free path of molecules in a gas will be halved if the pressure is doubled while the temperature is held constant.
Step-by-step explanation:
The mean free path of molecules in a gas is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure. In this case, if the pressure is doubled while the temperature is held constant, the mean free path will be halved.
Let's say the mean free path of molecules in the gas at the initial pressure is 200nm. When the pressure is doubled, the new pressure is twice the initial pressure. Therefore, the new mean free path will be half of the initial mean free path, which is 100nm. So, the mean free path will be 100nm if the pressure is doubled while the temperature is held constant.
When considering the mean free path of molecules in a gas, it's important to understand the relationship between pressure and volume when the temperature is held constant, as described by the ideal gas law (PV = NkT).
The mean free path is the average distance a molecule travels between collisions, and it is inversely proportional to the pressure, assuming temperature and volume remain constant. Therefore, when the pressure is doubled, the mean free path is halved. So, if the initial mean free path is 200nm, doubling the pressure while keeping the temperature the same would result in a mean free path of 100nm.