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?

2 Answers
Mar 5, 2018

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

Mar 5, 2018

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.