In a 3 x 10 9 -year-old rock that originally contained some 238 U, which has a

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In a 3 x 109 -year-old rock that originally contained some 238U, which has a half-life of 4.5 x 109 years, we expect to find some 238U remaining in it. Why are 226Ra, 222Rn, and 210Po also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)?

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