Radioactive element X has a half-life of 30 days. A rock sample contains 4 grams element X when it forms. How many half-lives will have elapsed in 90 days? How much of the original amount of X will be unchanged after 90 days?

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Answer 1 · 2018-07-19T18:32:33

#3# & #0.5\ gm#

Given that radioactive element X has a half-life #30# days

Hence the number #(n)# of half-lives in #90# days

#n=90/30#

#n=3#

The amount #N# of radioactive element X left after #n=3# half-lives with initial amount #N_0=4\ gm#

#N=N_0(1/2)^n#

#=4(1/2)^3#

#=4/8#

#=0.5#

hence the amount left after #90# days or #3# half-lives will be #0.5# grams