To solve this problem, we first need to understand the properties of the materials involved and the formulas related to them. The resistivity of tungsten is 5.60 x 10^-8 ohm meters. The resistance of this particular length of tungsten is given as 0.26 ohms and its length is 1.00 meter.
The resistance (R) of a wire can be calculated using the formula R = rho * (L/A) where rho is the resistivity, L is the length, and A is the cross-sectional area. In order to find the cross-sectional area first, we will rearrange the formula to A = rho * (L/R). Substituting the known values, we get:
A = 5.60 x 10^-8 * (1.00 / 0.26), which equals roughly 2.15 x 10^-7 square meters.
Given the area, we can now calculate the diameter of the wire. The cross-sectional area of a wire is also equal to pi*(d/2)^2, where d is the diameter of the wire. By rearranging this formula, we get d = 2*sqrt(A/pi). Therefore, substituting the calculated area into this formula gives:
d = 2 * sqrt(2.15 x 10^-7 / pi), which equals about 0.00052 meters or, equivalently, 0.52 millimeters, with the result rounded to two significant figures.
So, the diameter of the tungsten wire is approximately 0.52 mm.