Final answer:
To find the diameter of a capillary tube, you can use the capillary rise method, considering the height to which water rises and factors such as surface tension, contact angle, density of water, and gravity.
Step-by-step explanation:
To determine the diameter of a capillary tube, one must understand the principles of capillarity and the equation that relates the rise of water in the tube to its diameter. The height to which water rises in a capillary tube (capillary action) is inversely proportional to the diameter of the tube and depends on the cohesive and adhesive forces between the water molecules and the tube's material. If water rises up to a height of 8.4 cm in the tube, we can use the equation given by the capillary rise method, or the Jurin's Law equation, which is h = (2γcosθ)/(ρgd) where h is the height the liquid rises, γ is the liquid-air surface tension, θ is the contact angle, ρ is the density of the liquid, g is the acceleration due to gravity, and d is the diameter of the tube. Calculations would involve rearranging the formula to solve for d and substituting the known values for the constants and variables.