Suppose that a certain radioactive element decays in such a way that every twenty years the mass of a sample of the element is one third of the initial mass. Given a 100 gram sample of the element, how much of the element remains after 17 years

Therefore 21.09 gram of the element remains after 17 years.

Step-by-step explanation:

The decay rate is proportional to the number of nuclei.

Integrating both sides

Initially N= , when t=0

The equation becomes

N= Remaining mass after t time

= initial mass of the sample

= decay constant

Given that, every 12 years the mass of a sample of a the element is one third of the initial mass.

Here, , t= 12 years

           [ ]

                     [ and ]

The equation becomes

Given that, the initial amount and t =17

gram

Therefore 21.09 gram of the element remains after 17 years.

6 cm

step-by-step explanation: