Final answer:
To estimate the size of one cell in micrometers, take the field of view at x400 magnification, which can be approximately derived from the known x100 field of view, and divide it by the number of cells that fit across it (10). This assumes the field of view size remains constant when changing magnifications, which is not strictly accurate but serves for a rough estimation.
Step-by-step explanation:
To estimate the length of one cell in micrometers when 10 cells line up across a field of view at x400 magnification, we first need to understand that microscopes are tools used in biology to magnify cells so we can see them better. Light microscopes commonly used in college biology labs magnify up to approximately 400 times and a typical human red blood cell is about eight micrometers (um) in diameter. It's important to realize that the total magnification of a microscope is determined by multiplying the magnification of the objective lens by that of the ocular lens, usually 10x for the latter.
If 10 cells fit across the field of view at x400 magnification, and we know the magnification level, we can determine the approximate size of one cell. Since the field of view is not provided in actual measurement units, we will use the fact that at x100 magnification the student saw 'x' field of view.
Assuming the same field of view size for x100 and x400 magnifications (although this is not completely accurate as field of view decreases with increased magnification), if we divide the field of view size at x100 by 4 (since x400 is four times the magnification of x100), we would get the field of view size at x400. Then, if 10 cells fit across this distance, we divide the field of view at x400 by 10 to find the estimated size of one cell.