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# $$^{238}U$$ decays to $$^{206}Pb$$ with a half-life of $$4.47 \times 10^9$$y. this happens in a number of steps.Can you justify a single half-life for this chain of processes ? A sample of rock is found to contain 2.00 mg of $$^{238} U$$ and 0.600 mg of $$^{206}Pb$$ assuming that all the lead has come from uranium, find that life of the rock .

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Q1
$$^{238}U$$ decays to $$^{206}Pb$$ with a half-life of $$4.47 \times 10^9$$y. this happens in a number of steps.Can you justify a single half-life for this chain of processes ? A sample of rock is found to contain 2.00 mg of $$^{238} U$$ and 0.600 mg of $$^{206}Pb$$ assuming that all the lead has come from uranium, find that life of the rock .
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Q2
238U decays to 206Pb with a half-life of 4.47 × 109 y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.
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Q3

238U decays to 206Pb with a half-life of 4.47×109. This happens in a number of steps. Can you justify a single half-life for this chain of process ? A sample of rock is found to contain 2.00 mg of 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.

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Q4
The isotope $$^{238}U$$ decays to $$^{206}Pb$$ with a half-life of $$4.47 \times 10^9 y$$.Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead.That is,
$$^{238}U \rightarrow ^{206}Pb$$ + various decay products
A rock is found to contain 4.20 mg of $$^{238}U$$ and 2.135 mg of $$^{206}Pb$$.
Assume that the rock contained no lead at formation, so all the lead now present arose from the decay of uranium. How many
atoms of (a) $$^{238}U$$ and (b) $$^{206}Pb$$ does the rock now contain? (c) How
many atoms of $$^{238}U$$ did the rock contain at formation? (d) What is the age of the rock?

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Q5
A rock recovered from far underground is found to con-tain 0.86 mg of 238U, 0.15 mg of $$^{206}Pb$$, and 1.6 mg of $$^{40}Ar$$. How much $$^{40}K$$ will it likely contain? Assume that $$^{40}K$$ decays to only $$^{40}Ar$$ with a half-life of $$1.25 \times 10^9 y$$. Also assume that $$^{238}U$$ has a half-life of $$4.47 \times 10^9 y$$.
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