The half-life of radioactive iodine is 60 days. How much of a 50-mg sample will be left in 40 days? Round your answer to the nearest tenth.

Question

asked Aug 22, 2021 171k views

2 Answers

Antonio Dias · Answer 1 · 2021-08-29T08:35:48+0000

Answer:

Remaining amount of the element = 31.5 mg

Explanation:

Half life of radioactive Iodine is
$(T_{(1)/(2)})$ = 60 days

Formula to get the remaining element after t days is,

$N=N_0(e)^(\lambda.t)$

Where
$\lambda$ = decay constant of the radioactive element

t = duration of the decay (in days)

N_0 = Initial amount of the element

N = final amount after decay

For half life period 't' = 60 days

$(N_0)/(2)=N_0(e)^(\lambda* 60)$

$e^(60\lambda)=0.5$

$ln(e^(60\lambda))=ln(0.5)$

$60\lambda =-0.069315$

$\lambda=-0.0115524$

Remaining amount of the element after 40 hours,

N =
$50(e^(40\lambda) )$

=
50(e)^(-(0.0115524)* 40)

= 50(0.62996)

= 31.49

≈ 31.5 mg

Therefore, remaining amount of the element after 40 days is 31.5 mg.