a. If a substance has D=1.0×10^{−9} m^{2} s^{−1}, find the root-mean-square distance diffused in 1.00 hour.
b. In the random walk model an object repeatedly takes a step of fixed length in a randomly chosen direction. The root-mean-square distance traveled in one dimension is equal to the square root of the number of steps, N, times the length of a step, denoted by a: d_{rms}=\sqrt{N }a. If a molecule moves 6×10^{−10} m each time it moves to a new cage and if it requires 1 hour to diffuse the distance found in the previous example, estimate the time required to move to a new cage.