At 1:00 pm I measure 10 grams of the element, but at 1:24 pm I measure only 1.25 grams of the element (with 8.75 grams of daughter product). How long is each half life, in minutes? (Just enter the number).

The half life of the element = 8 minutes

Explanation:

Solution:

The initial amount = 10g

final amount = 1.25g

elapsed time = 24 minutes

Half life formula

t1/2 = t / (log1/2 (Nt/N0))

or (Nt/N0) = 0.5^ (t / (t1/2))

or 1.25/10 = 0.5^ ((24*60) / (t1/2))

Log of both sides gives

0.125 = 0.5^ (1440 / (t1/2))

-0.903 = 1440/t1/2*log (0.5)

-0.903 = 1440/t1/2 * (-0.301)

3 = 1440/t1/2

t1/2 = 1440/3 = 480

Solving we have

t1/2 or the half life = 480s

= 480/60 minutes or

= 8 minutes