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?

Mar 7, 2016

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"

$A = {A}_{0} / {2}^{n} = \text{30 counts"/2^8 = "0.117 counts}$