To clarify the answer to your original question....Dividing the Focal length by the f-number does not determine the aperture diameter, it determines the apparent diameter of the aperture, when viewed through the front lens elements (this is known as the Lens Pupil).
Imagine using a magnifying glass to view a hole in a piece of paper. Move the magnifying glass backwards and forwards and the hole increases, or decreases in size. That is what is happening when you change focal lengths. The aperture stays the same physical size at the same f-number, but when viewing it through the front lens elements its apparent size changes according to focal length.
So, the aperture does not physically open up to 9.8mm, or reduce to 6.86mm. It is just the rearrangement of the lens elements at different focal lengths causing the change.
Sark