Physics, 13.10.2019 19:00 geraldsmith2008

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

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Answer from: steven122048i

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

Answer from: Quest

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by mathematical calculations before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of uranus led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.

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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...