Question

Lead-202 has a half-life of 53,000 years. How long will it take for 15/16 of a sample of lead-202 to decay?


A) 106,000 years

B) 159,000 years

C) 212,000 years

D) 265,000 years

Answer 1

The answer to this question is 

C. 212,000 years

Saucy out 

Answer 2

Answer:

C) 212,000 years

Explanation:

The half-life of a radioactive sample is the time it takes for half of the sample to decay.

In this case, the half-life is 53,000 years: this means that after 53,000 years, half of the sample will decay. So we will have:

- After 1 half life (53,000 years): 1/2 of the sample has decayed, so 1/2 is left undecayed

- After 2 half-lives (106,000 years): since the amount left is now 1/2, the amount that decay now is $\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$. So the total amount decayed is now $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$, and the amount left is $\frac{1}{4}$

- After 3 half-lives (159,000 years): since the amount left is now 1/4, the amount that decay now is $\frac{1}{2} \cdot \frac{1}{4}=\frac{1}{8}$. So the total amount decayed is now $\frac{3}{4}+\frac{1}{8}=\frac{7}{8}$, and the amount left is $\frac{1}{8}$

- After 4 half-lives (212,000 years): since the amount left is now 1/8, the amount that decay now is $\frac{1}{2} \cdot \frac{1}{8}=\frac{1}{16}$. So the total amount decayed is now $\frac{7}{8}+\frac{1}{16}=\frac{15}{16}$, and the amount left is $\frac{1}{16}$

So, the correct answer is

C) 212,000 years