Question

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.

Answer 1

In 40 days, there would be approximately 31.5 mg remaining.

Explanation:

Answer 2

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.