How many milligrams of a 15.0 mg sample of radium-226 remain after 6396 years if the half-life of radium-226 is 1599 years?

1 Answer
May 24, 2018

Answer:

#0.9375mg#

Explanation:

#6396/1599 = 4#

the half life of radium-226 is #1599# years, so after #6396# years, #4# half-lives will have passed.

#1# half-life is the time taken for the mass of the sample of radium-226 to halve, or multiply by #1/2#.

#4# half-lives is the time taken for the mass of radium-226 to halve #4# times, or multiply by #(1/2)^4#.

#(1/2)^4 = 1/16#.

this means that after #4# half-lives, #1/16# of the original sample will be left.

#1/16 * 15.0mg = 0.9375mg#