Question

The half-life of a certain radioactive substance is 14 days. There are 6.6g present initially. Express the amount of substance remaining as a function of time t.

Answer 1

Quantity remaining after some time has passed can be represented by

\[Q(t) = Q(0) 2^{-t/k}\]where \(Q(0)\) is the initial amount, t is the elapsed time, and k is the half-life (measured in the same units as the time).

At t = 0, the formula reduces to \[Q(0) = Q(0)*2^{-0/k} = Q(0) *2^0 = Q(0)\]all of the initial quantity is still present.

At t = k (1 half life), the formula gives \[Q(k) = Q(0)*2^{-k/k} = Q(0)*2^{-1} = Q(0)*\frac{1}{2}\]1/2 of the initial quantity is present.

At t = k (2 half lives), the formula gives \[Q(2k) = Q(0)*2^{-2k/k} = Q(0)*2^{-2} = Q(0)*\frac{1}{4}\]1/4 of the initial quantity is present