The radioactive element that gradually decays to lead and can be used to date ancient rocks.

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Chapter 24, Problem 10MC

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The radioactive element that gradually decays to lead and can be used to date ancient rocks.

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You are dating rocks by their proportions of parent isotope potassium-40(half life 1.25 billion years) and daughter isotope argon-40. Find the age for a rock that contains 3 times as much Argon-40 as potassium 40. Needs Complete solution with 100 % accuracy.

SOME ISOTOPES USED FOR RADIOMETRIC DATING Daughter Isotope (D) Half-Lives (T½) Useful Dating Range Parent Isotope (P) Materials Dated Newly formed crystal Uranium-238 4.5 billion years Zircon 713 million years Zircon Lead-206 ages > 10 m.y. 100 Uranium-235 Lead-207 ages > 10 m.y. 0000000o o00000 15.9% decayed to daughter Potassium-40 Argon-40 Biotite, muscovite, whole volcanic rock 1.3 billion years ages > 50,000 yr Shells, limestone, organic materials ages 100-60,000 yr Carbon-14 Nitrogen-14 5730 years 84.1 29.3% decayed 70.7 Parent Atoms (P) 000000000e 50% decayed RADIOACTIVE DECAY 50.0 Daughter Atoms (D) 25.0 75% decayed 87.5% decayed 12.5 93.8% decayed 96.9% decayed 6.2 3.1 14 2 3 4 5 6 Half-Lives (T1) Elapsed DECAY PARAMETERS FOR ALL RADIOACTIVE DECAY PAIRS Percent of Parent Atoms (P) Percent of Daughter Atoms (D) Half-Lives Elapsed Age 0.000 x T 0.015 x T 0.031 x Ty 0.062 x Ty 0.125 x T 0.250 x T 0.500 x T2 1.000 x Ty2 100.0 0.0 98.9 1.1 1/64 97.9 2.1 1/32 95.8 4.2 1/16 91.7 8.3…

Uranium-lead (U-Pb) dating of geological samples is one of the oldest and most refined radiometric dating methods, able to determine ages of about 1 million years to over 4.5 billion years with precision in the 0.1–1% range. The U-Pb dating method relies on two separate decay chains, one of which is the actinium series from 235U to 207Pb, with a half-life of 704 million years. Geologists unearth a sample of zircon that appears to be a closed system. They find 0.714 grams of 207Pb for 1.000 grams of 235U present. Approximately how old is the sample? _______ yrs