Question

A sample of a radioactive isotope emits particles at a rate of 240 per minute. After 48 hours the rate of emission has decreased to 15 per minute. What is the half-life of the radioactive material?

Answer 1

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Answer 2

The half-life of the radioactive material is 12 hr.

Explanation:

The relationship between the original number of nuclei present at time $(N_0)$zero and the number (N) at a later time t:

$N=N_0(\frac{1}{2})^\frac{t}{t_{1/2} }$

Here, $t_{1/2}$ is half life of the materail.

Given  $N=15 / min$ and $N_0 =240/min$.

substitute the values, we get

$15=240(\frac{1}{2})^\frac{t}{t_{1/2} }$

$\frac{1}{16} =(\frac{1}{2})^\frac{t}{t_{1/2} }$

$\frac{t}{t_{1/2} }=4$

Given t = 48 hr

so,

$\frac{48hr}{t_{1/2} }=4$

$t_{1/2}=\frac{48hr}{4}=12hr$

Thus, the half-life of the radioactive material is 12 hr.

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