Question

lutetium-176 has a half-life of 3.85 × 10¹⁰ years. after 1.155 × 10¹¹ years, how much lutetium-176 will remain from an original 16.0-g sample?
○ 2.10 g
○ 3.00 g
○ 5.55 g
○ 8.40 g

Explanation:

Answer:

First, find the number of half - lives \(n\) passed. The formula for the number of half - lives is \(n=\frac{t}{T_{1/2}}\), where \(t = 1.155\times10^{11}\) years and \(T_{1/2}=3.85\times10^{10}\) years.

\(n=\frac{1.155\times 10^{11}}{3.85\times 10^{10}}=\frac{11.55\times10^{10}}{3.85\times 10^{10}} = 3\)

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0 = 16.8\) g is the initial amount, and \(n = 3\) is the number of half - lives.

\(N=16.8\times(\frac{1}{2})^3=16.8\times\frac{1}{8}=2.10\) g

So the answer is 2.10 g.