Here we're told that the radioactive element of Acetene 210 has a decay constant of 0.086 hours-1. Inverse, how many minutes would it take for its concentration to go from 9.3 * 105 disintegrations per second to 2.7 * 104 disintegrations per second? All right, so they wanted to find minutes, so they're asking us to find time. Our variable T is the missing variable.

All right, so we're going to have our radioactive integrated rate law, which remember would be lane of our final concentration. Remember, concentration here doesn't necessarily mean molarity in this case, it's a disintegration per second and that's fine, minus KT plus lane of our initial concentration. Remember, your final concentration should be the smaller total because we're decreasing our amount of reactant over time as it's decaying away.

So lane of 2.7 * 104 disintegrations per second are the K constant. K we're told is -0.086 hours-1. Inverse, we don't know what T is. That's what we need to find plus lane of our initial, which is the larger amount. Subtract Ln of 9.3 * 105 from both sides. When we do that, we're going to get Initially 353934772 equals negative 086 hours-1 times T.

Divide both sides by your K value and we it's important to keep the units around so we can see what our units will be at the end. At the end time is in hours, but remember I want the answer in minutes, so we have to do one last conversion. Remember that one hour is equal to 60 minutes. So time here would be equal to 2.5 * 103 minutes. This would be our final answer.