a sample contains 10.5 g of the radioisotope pb - 212 and 157.5 g of its daughter isotope, bi - 212. how…
a sample contains 10.5 g of the radioisotope pb - 212 and 157.5 g of its daughter isotope, bi - 212. how many half - lives have passed since the sample originally formed?\n4\n14\n15\n147.5
Answer
Explanation:
Step1: Calculate the total mass originally
The total mass originally is the sum of the current mass of the radioisotope and its daughter - isotope. So, the original mass $m_0=10.5 + 157.5=168$ g.
Step2: Calculate the fraction of the remaining radioisotope
The fraction of the remaining radioisotope $N/N_0=\frac{10.5}{168}=\frac{1}{16}$.
Step3: Use the half - life formula
The formula for radioactive decay is $N = N_0(\frac{1}{2})^n$, where $N$ is the current amount of the radioisotope, $N_0$ is the original amount, and $n$ is the number of half - lives. We know that $\frac{N}{N_0}=(\frac{1}{2})^n$. Since $\frac{N}{N_0}=\frac{1}{16}=(\frac{1}{2})^4$, then $n = 4$.
Answer:
4