Question

Phosphorous-32 has a half life of 14.3 days. A 30-count sample is stored for 114.4 days. How much radiation remains in the original sample?

Answer 1

After 114.4 days, the count will be 0.117.

Explanation:

The formula for calculating the amount remaining after a number of half-lives, `n` is

`color(blue)(|bar(ul(A = A_0/2^n )|)`

where `A_0` is the initial amount and `A` is the amount remaining.

`n = 114.4 cancel("days") × "1 half-life"/(14.3 cancel("days")) = "8 half-lives"`

`A = A_0/2^n = "30 counts"/2^8 = "0.117 counts"`