Question

the half - life of u - 238 is 4.5 billion years (the age of the earth). what fraction of u - 238 present when earth formed still remains? start a 1/2 if 100 g of au - 19 to 6.25 g

Explanation:

Step1: Recall the half - life formula

The formula for the amount of a radioactive substance remaining after \(n\) half - lives is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount and \(N\) is the final amount. Here, the age of the Earth is equal to one half - life of \(U - 238\) (\(n = 1\)).

Step2: Substitute \(n = 1\) into the formula

When \(n = 1\), we have \(N=\frac{N_0}{2}\). So the fraction of \(U - 238\) remaining is \(\frac{1}{2}\).

Answer:

\(\frac{1}{2}\)