The gas-phase decomposition of ozone, \(\text{O}_3(g)\), proceeds according to the overall balanced equation:

\[2\text{ O}_3(g) \rightarrow 3\text{ O}_2(g)\]

A proposed two-step mechanism for this reaction is shown below:

\[\text{Step 1: } \text{O}_3(g) \rightleftharpoons \text{O}_2(g) + \text{O}(g) \quad \text{(fast equilibrium)}\]
\[\text{Step 2: } \text{O}_3(g) + \text{O}(g) \rightarrow 2\text{ O}_2(g) \quad \text{(slow)}\]

In an initial experiment, the reaction is initiated with \([\text{O}_3]_0 = 0.020 \text{ M}\) and \([\text{O}_2]_0 = 0.010 \text{ M}\), giving an initial rate of \(R_1\).

In a second experiment at the same temperature, the reaction is initiated with \([\text{O}_3]_0 = 0.040 \text{ M}\) and \([\text{O}_2]_0 = 0.020 \text{ M}\), giving an initial rate of \(R_2\).

Based on the proposed mechanism, what is the value of the ratio of the new initial rate to the original initial rate, \(\dfrac{R_2}{R_1}\)?