Final answer:
Due to a lack of sufficient data, such as a time interval or multiple data points, we cannot accurately calculate the reaction rate at time t = 0 based on the information provided.
Step-by-step explanation:
The student is asked to calculate the rate of reaction at time t = 0. Using the data provided, the rate of reaction is the change in diameter per unit time (rate = ∂diameter/∂time). We have the initial diameter (d0) as 5.0×10-5 m and the diameter at t = 3 seconds (d_3) as 3.0×10-4 m. To find the rate at t = 0, we calculate the change in diameter divided by the time interval. However, since no time interval other than t = 0 is given for the calculation of initial rate and the change in diameter is not provided for a particular time, it's not possible to calculate the rate directly from this data. A standard approach in kinetics is to use the rate equation or to have multiple data points to calculate the rate at t = 0. Therefore, based only on the given information, there isn't sufficient data to calculate an accurate reaction rate.