physical science

Question

A specific radioactive isotope as a half-life of 33.2 minutes. How long will it take this isotope to decay to 1/8 of its original amount?

Answer 1

The general formula to calculate the number of half lives it would take for a substance to decay to a certain percentage of the original amount is given by the following formula:

 

(1/2)^n = proportion of the original amount left

 

in this case,    (1/2) ^ n = 1/8

 

                      (1/2)^ n = 0.125

 

or,     n*log (0.5) = log 0.125

 

         n = log 0.125/log 0.5

 

         n = 3

 

Therefore, it would take 3 half-lives for the isotope to decay to 1/8 of its original amount.

 

Since half-life is given as 33.2 minutes

 

3 Half-lives would equal 3*33.2 = 99.6 minutes

Answer 2

Sorry, I used the wrong half-life when I posted originally.  Since the problem is given as a power of (1/2), it is trivially easy.  One half-life, 1/2.  Two half-lifes, 1/4.  Three half-lifes, 1/8.  

 

3 half-lifes = 3 x 33.2 minutes = 99.6 minutes

 

If the question has been 1/10 of the original amount, you would have to resort to an exponential equation.