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:

$\overline{){\mathbf{ln}}\mathbf{\left(}\mathbf{rate}\mathbf{\right)}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}\mathbf{(}\mathbf{initial}\mathbf{}\mathbf{rate}\mathbf{)}}$

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

A sample containing a radioactive isotope produces 2000 counts per minute in a Geiger counter. After 120 hours, the sample produces 250 counts per minute. What is the half-life of the isotope?

A. 60 h

B. 15 h

C. 20 h

D. 30 h

E. 40 h

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