The radioactive element thorium-234 has a half-life of approximately 24 days. If I started with 82 grams of it, how much thorium would remain after 96 days?

1 Answer
Junaid Mirza
Jun 5, 2018

#"5.125 g"#

Explanation:

If #96# days is #"n"# half lives then

#"n" = "96 days"/("24 days/half life") = "4 half lives"#

Amount of radioactive substance left after #"n"# half lives is given by

#"N"_t = "N"_0/(2^"n")#

Where

  • #"N"_0 =#Initial Amount
  • #"N"_t =#Amount left after #"n"# half lives
  • #"n ="# Number of half lives

#"N"_t = "82 g"/2^4#

#color(white)("N"_t) = "82 g"/16#

#color(white)("N"_t) = "5.125 g"#

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