{"knowledge_schema": {"broad_category": "Physics \u2192 Vacuum Technology \u2192 Mean Free Path", "refinement": "This problem examines the behavior of gas molecules in a vacuum and their interaction with an electron beam, focusing on the concept of mean free path.", "specific_scope": "The context involves comparing the mean free path of gas molecules in a vacuum (\u03bb1) with the mean free path of electrons interacting with those gas molecules (\u03bb2) in a high-resolution electron microscope.", "goal": "Determine the relationship between the mean free paths \u03bb1 and \u03bb2 based on the presence of gas molecules and their interaction with the electron beam."}, "summary": "In this problem, we analyze the mean free path of gas molecules in a vacuum (\u03bb1) and the mean free path of electrons interacting with those gas molecules (\u03bb2) in a high-resolution transmission electron microscope. Given that \u03bb1 represents the distance gas molecules travel before colliding with each other, and \u03bb2 represents the distance electrons travel before scattering off gas molecules, we conclude that \u03bb2 is less than \u03bb1 (\u03bb2 < \u03bb1) due to the increased likelihood of scattering events when electrons encounter gas molecules."}