Question

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

Answer 1

Approximately 5 grams of an 80 gram sample of xenon-133 would be left after 20.8 days.

Step-by-step explanation:

To determine how much of the xenon-133 sample would be left after 20.8 days, we need to calculate the number of half-lives that have occurred. The formula to calculate the remaining amount is:

Remaining amount = Initial amount imes (1/2)ⁿ

In this case, the initial amount is 80 grams and the half-life of xenon-133 is 5.2 days. Therefore, the number of half-lives is given by:

Number of half-lives = (20.8 days) / (5.2 days per half-life) = 4

Plugging the values into the formula, we have:

Remaining amount = 80 g imes (1/2)⁴ = 80 g imes (1/16) = 5 g

Therefore, approximately 5 grams of the 80 gram sample would be left after 20.8 days.

Answer 2

6.73g

Step-by-step 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