Even when a mechanism is consistent with the rate law , later experimentation may it to be incorrect or only one of several alternative. As an example, the reaction between hydrogen and iodine has the following rate law: rate=k[H]^3[I]2.

Question

Even when a mechanism is consistent with the rate law , later experimentation may it to be incorrect or only one of several alternative. As an example,  the reaction between hydrogen and iodine has the following rate law: rate=k[H]^3[I]2.
The long accepted mechanism proposed a single
Biomolecular step,  that is, the overall reaction was though to be elementary:
H2(g)+i2(g)-> 2HI (g)
In the 1960's, however,  spectroscopy evidence showed the presence of free I atom during the reaction kineticists have since proposed a three step mechanism:
(1) I ^2(g)<-> 2i (g) [fast]
(2) H^2(g)+I(g)->H^2I (g)[fast]
(3)H^2i (g)+I(g)-> 2HI (g) [slow]
Show that this mechanism is consistent with the rate law.