Question

One mole of a parent nuclide is undergoing radioactive decay. The fraction of atoms of this nuclide that has decayed after three half-lives is.................

Hint:

The fraction of atoms decayed in radioactive decay can be calculated using the formula \(1 - \left(\frac{1}{2}\right)^n\), where \(n\) is the number of half-lives.

Answer 1

Correct Answer: 0.875

Step 1. The fraction of the nuclide that has decayed after \(n\) half-lives is given by the formula:
\[ \text{Fraction decayed} = 1 - \left( \frac{1}{2} \right)^n \]

Step 2. For three half-lives (\(n = 3\)):
\[ \text{Fraction decayed} = 1 - \left( \frac{1}{2} \right)^3 = 1 - \frac{1}{8} = 1 - 0.125 = 0.875 \]
Thus, the fraction of atoms that has decayed after three half-lives is 0.875.
\[ \boxed{0.875} \]