Question

If 32.3g of a radioisotope decays to 19.2g, what is the half-life of the radioisotope?

a) 10.7 years
b) 15.4 years
c) 7.6 years
d) 8.9 years

Answer 1

The half-life of the radioisotope is approximately 32.4 years.

Step-by-step explanation:

The half-life of a radioisotope is the amount of time it takes for half of the sample to decay. To find the half-life, we can use the formula t1/2 = (-0.693 / λ), where λ is the decay constant. The decay constant can be calculated by taking the natural logarithm of 2 and dividing it by the half-life period in years. Using the given information, we can calculate the decay constant and then determine the half-life:

t1/2 = (-0.693 / λ)

λ = (ln(2) / t1/2)

λ = (ln(2) / 32.3)

λ ≈ 0.0214

Now, we can substitute the decay constant into the formula for half-life:

t1/2 = (-0.693 / 0.0214)

t1/2 ≈ 32.4 years

Therefore, the half-life of the radioisotope is approximately 32.4 years.