Question #fca61

1 Answer
Dec 29, 2014

The answer is #62 days#.

We know that an exponential decay can be expressed mathematically by

#A(t) = A_0 * (1/2)^(t/t_("1/2"))#, where

#A(t)# - the amount left after t years;
#A_0# - the initial quantity of the substance that will undergo decay;
#t_("1/2")# - the half-life of the decaying quantity.

#"Ra-223"# has a molar mass of approximately #223g/(mol)#, which means that the sample's initial mass and the final mass will be

#A_0 = 0.240# #mol es * 223 g/(mol) = 53.5g#

#A(t) = 7.50 * 10^(-3)# # mol es * 223 g/(mol) = 1.67g#

So,

#1.67 = 53.5 * (1/2)^(t/12.4) -> 0.0312 = (1/2)^(t/12.4)#

#t/(12.4) = log_(0.5)(0.0312) = 5.002#, which means that

#t = 5.002 * 12.4 = 62# days.