The radioisotope xenon-133 has a half-life of 5.2 days. How much of an 80 gram sample would be left after 20.8 days? PLEASE SHOW YOUR WORK

6.73g

Explanation:

T½ = 5.2days

No = 80g

N = ?

T = 20.8days

We'll have to find the disintegration constant first so that we can plug it into the equation that will help us find the mass of the sample after 20.8 days

T½ = In2 / λ

T½ = half life

λ = disintegration constant

λ = In2 / T½

λ = 0.693 / 5.8

λ = 0.119

In(N / No) = -λt

N = final mass of the radioactive sample

No = initial mass of the sample

λ = disintegration constant

t = time for the radioactive decay

In(N/No) = -λt

N / No = e^-λt

N = No(e^-λt)

N = 80 × e^-(0.119 × 20.8)

N = 80 × e^-2.4752

N = 80 × 0.0841

N = 6.728g

The mass of the sample after 20.8 days is approximately 6.73g