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?

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Answer 1 · 2018-05-24T20:45:26

$0.9375mg$

$6396/1599 = 4$

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.

$1/16 * 15.0mg = 0.9375mg$