We are asked to **determine the half-life of the radioactive isotope which has a rate starting from 2000 min ^{-1 }to 250 min^{-1} after 120 hrs**

The * integrated rate law *for a 1st-order reaction is as follows:

$\overline{){\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{0}}}}$

where **rate**= rate at time t, **k** = rate constant, **t** = time, initial rate = starting rate

A first-order reaction has a rate constant of k = 0.320 min^{–1}. For an initial reactant concentration of 1.22 M, how long does it take for its concentration to fall to 0.150 M?

A. 2.60 min

B. 6.55 min

C. 25.4 min

D. 0.671 min

E. 18.3 min

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