PLEASE HELP WILL GIVE BRAINLIEST Xenon-133 has a half life of 5.2 days. A 237 gram sample of Xenon is collected and stored. It is later measured to be 29.625 grams. How long has it been in storage?
A. 15.6 days
B. 39.9 days
C. 20.8 days
D. 8 days

A. 15.6 days

Explanation:

We have a general formula used to solve for questions dealing with half life.

N(t) = No (1/2)^t/t½

Where

N(t) = Quantity of sample left after t days

No = Initial amount of sample

t½ = Half life of sample

t = Duration or time required for sample to decay

In the above question, we are asked to determine how long(time) that the sample has been in storage.

The formula for time (t) has been derived as:

t =[ t½ × In(Nt/No)] ÷ - In 2

Where

No = 237 grams

N(t) = 29.625 grams

t½ = 5.2 days

t = Unknown

t = [ t½ × In(Nt/No)] ÷ - In 2

t = [ 5.2 × In(29.625/237)] ÷ - In 2

t = [5.2 × -2.0794415417] ÷ - In 2

t = -10.813096017 ÷ - ln 2

t = 15.6 days

Therefore, the sample has been in storage for 15.6 days.

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