Question

A radioactive isotope of potassium (K) has a half-life of 20 minutes. If a 40.0 gram sample of this isotope is allowed to decay for 80 minutes, how many grams of the radioactive isotope will remain?

Answer 1

The mass is `=2.5g`

Explanation:

The equation for the radioactive decay is

`A(t)=A_0e^(-lambdat)`

where `lambda` is the radioactive constant

`lambda=(ln2)/t_(1/2)`

The half life of `"Potassium-40"` is `t_(1/2)=20mn`

The initial mass is `A_0=40.0g`

The time is `t=80mn`

Therefore,

The quantity remaining is

`A(t)=40e^((-(ln2)/20)*80)`

`A(t)=40e^(-2.7726)=2.5g`

Answer 2

As half life is 20 minutes, the half of the material will decay in each slot of 20 minutes,therefore after 80 minutes one will have only 2.5 grams of the sample left out of 40 grams.