A sample of a radioactive isotope decays at a rate of 988 disintegrations per minute. Exactly 85 minutes later the decay rate of the sample is 251 disintegrations per minute. What is the half-life of this isotope?

Question

Quizplus · Accepted Answer

The half-life of a radioactive isotope is the amount of time it takes for half of the sample to decay.

We can use the formula:

N(t) = N0*(1/2)^(t/T)

where N0 is the initial number of atoms, N(t) is the number of atoms at time t, T is the half-life, and t is the elapsed time.

We can set up two equations using the given information:

988 = N0*(1/2)^(85/T)

251 = N0*(1/2)^(170/T)

Dividing the second equation by the first equation, we get:

251/988 = (1/2)^(85/T)

Taking the logarithm of both sides and solving for T, we get:

T = -85 / (log(251/988) / log(1/2))

T ≈ 43.0 min

Therefore, the half-life of this isotope is about 43.0 minutes.

A Sample of a Radioactive Isotope Decays at a Rate