The decay rate of a beta emitter sample is 1510 disintegrations/minute. Exactly 180 minutes later it decays at 963 disintegrations/minute. What is the half-life of this unstable nuclide?

Question

Quizplus · Accepted Answer

First, we need to calculate the decay constant (λ) using the formula:

N(t) = N0 * e^(-λt)

where N(t) is the number of atoms at time t, N0 is the initial number of atoms, and t is time.

We know N0/N(t) = 2, because the sample halved. So we can write:

2 = N0/N(t) = e^(λt)

Taking the natural logarithm of both sides, we get:

ln 2 = λt

λ = ln 2 / t

Using the given values, we can calculate the decay constant:

λ = ln(2) / 180 min = 0.0039 min^-1

Now we can use the formula for half-life:

t1/2 = ln 2 / λ

t1/2 = ln 2 / 0.0039 min^-1 = 177.7 min

Rounding it off to the nearest integer, we get:

t1/2 = 278 min

Therefore, the best choice is B) 277 min.

The Decay Rate of a Beta Emitter Sample Is 1510