half life question

Question

the half-life of a substance is 12 minutes. If there are 100 mg initially, how much of the substance remains after 30 minutes?

 

I really struggle with the half life problems, do you have some helpful advice for me?

 

Answer 1

The simplest way to do this, in my humble opinion, is to use the following equation:

Fraction remaining = 0.5ⁿ where n = # of half lives that have elapsed.

30 min/12 min = 2.5 half lives have elapsed.

Fraction remaining = 0.5^2.5

Fraction remaining = 0.17678

Since you started with 100 mg, and the fraction remaining is 0.17678, the mg remaining = 100mg x 0.17678 = 17.7 mg (this is correct to 3 significant figures)

Answer 2

a = 100(0.5)^30/12

a = 100(0.5)^2.5

a = 100(0.176776695)

a = 17.6776695