Question

Question #444dd

Answer 1

The half life is 10.7 h.

Explanation:

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"`