Question

If the half life of Pb-210 is 22 years. How much of the original amount of Pb-210 remains after 88 years?A. 12.5%B. 25%C. 6.25%D. 50%

Answer 1

For this problem, we are told the half-life of a certain chemical element, we need to determine how much will be left of the original amount after 88 years.

We can model the exponential decay of an element with the following expression:

`N(t)=N_0\cdot2^{(-t)/(t_(1/2))}`

Where N(t) is the weight of the element after the elapsed time t, N0 is the initial amount and t 1/2 is the half-life of the substance. For this case we have:

`N(t)=N_0\cdot2^{(-t)/(22)}`

We can rewrite the expression as shown below:

`\begin{gathered} (N(t))/(N_0)=2^{(-88)/(22)}\\ \\ (N(t))/(N_0)=2^(-4)\\ \\ (N(t))/(N_0)=(1)/(16)=0.0625\\ \end{gathered}`

The amount that will remain after 88 years is approximately 6.25%. The correct answer is C.