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

C) 212,000 years

Step-by-step 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
`(1)/(2) \cdot (1)/(2)=(1)/(4)`. So the total amount decayed is now
`(1)/(2)+(1)/(4)=(3)/(4)`, and the amount left is
`(1)/(4)`

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

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

So, the correct answer is

C) 212,000 years