Question

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).

Answer 1

Answer:

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