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Answer 1 · 2017-05-28T19:19:36

The half life is 10.7 h.

The integrated rate law for radioactive decay is

$ln(A_0/A_t) = kt$

where

$A_0$ and $A_t$ are the activities at time $t = 0$ and at time $t$
$k$ is the decay constant
$t$ is the time

∴ $ln((9000 color(red)(cancel(color(black)("Bq"))))/(400 color(red)(cancel(color(black)("Bq"))))) = 3.114 = k × "2 days"$

$k = 3.114/"2 days" = "1.557 day"^"-1"$

$t_(1/2) = ln2/k = ln2/"1.557 day"^"-1" = "0.4453 days" = "10.7 h"$