Radioactive Decay Rate: Comparing Half-Lives

[accountkiller]

Homework Statement

You have two samples that exhibit radioactive decay. The first gives you initially a 1000/s decay rate and after one hour a 500/s decay rate. The second gives you initially a 500/s decay rate and after one hour a 250/s decay rate. Which sample has a higher probability per unit time that any nucelus will decay?

Homework Equations

λ = probability per unit time
N(t) = N₀e^-λt
T_mean = 1/λ = T_1/2/ ln(2)
-dN(t)/dt = λN(t)

The Attempt at a Solution

Does half-life mean the time it takes for the quantity of nuclei to be cut in half, or the time it takes for activity to be cut in half? I thought it was quantity, but the answer to this question is that the probability per unit time is the same for both, so I don't understand why.

-dN(t)/dt = 1000/s
-dN(t)/dt = λN(t) .. but I don't know N(t), so how do I find λ?

Am I just supposed to know that if the activity decreases by half in both, the probability is the same?

 

[accountkiller]

Wait.. -dN(t)/dt = λN(t) means that the activity is proprtional to the amount of nuceli.. so just from that equation, halving the activity is proportional to halving the amount, so same half-life, so same probability.

Never mind.

Can someone delete this thead? :)