For a reaction $$A \rightarrow 2B + C$$, the half lives are $$100 \text{ s}$$ and $$50 \text{ s}$$ when the concentration of reactant A is $$0.5$$ and $$1.0 \text{ mol L =}$$ respectively. The order of the reaction is ______.

We are given that for the reaction $$A \rightarrow 2B + C$$, the half-lives are 100 s and 50 s when the concentrations of A are 0.5 and 1.0 mol L$$^{-1}$$ respectively.

For an nth-order reaction, the half-life is related to initial concentration by:

$$t_{1/2} \propto [A_0]^{1-n}$$

The ratio of half-lives is:

$$\frac{t_{1/2}^{(1)}}{t_{1/2}^{(2)}} = \left(\frac{[A_0]_1}{[A_0]_2}\right)^{1-n}$$

$$\frac{100}{50} = \left(\frac{0.5}{1.0}\right)^{1-n}$$

$$2 = \left(\frac{1}{2}\right)^{1-n}$$

Rewriting,

$$2^1 = 2^{-(1-n)} = 2^{n-1}$$

It follows that

$$1 = n - 1$$

$$n = 2$$

Therefore, the correct answer is 2.