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File Edit View History Bookmarks People Window Help Microsoft Corporation [US] https://outlook.office.com/owa/?realm-radford.edu&path-;/a Mi Print Show email Geologic record: (XX). Uranium to Lead decay, 23U to 207Pb, is often used to date the ages of very old rock formations. When zircon forms it incorporates Uranium, but not lead, so we can assume that the initial crystals of zircon have no lead. The half-life of the U to2Pb decay process is 710 million years. (a, 2 pts) If there are 10 times more Lead-207 atoms as Uranium-235 atoms in a zircon crystal, provide a minimum and maximum age (based on the number of half- lives you infer occurring) of the crystal. Between and Million years old There is a second type of radioactive decay, 23U to 20Pb, which has a half-life of 4.47 billion years (b, 2 pts) Assume that a deposit of Uranium-238 becomes isolated 2.235 billion years ago and is recently discovered. Will the amount of Uranium-238 that has decayed be more or less than 25%? Explain your reasoning. (xx) COMPOUND INTEREST. Imagine that you have a loan with an initial balance ofExplanation / Answer
Answer (a)
Half-life of Uranium-235 to Lead-207 decay is 710 million years.
Number of Lead-207 atoms is 10 times more than that of Uranium-235 atoms.
With every passing 710 million years, the number of Uranium atoms will be halved relative to the starting amount, and the same number of Lead atoms will be yielded.
After passage of 0 half-lives, we will have 100 Uranium-235 atoms & 0 Lead-207 atoms
After passage of 1 half-live, we will have 50 Uranium-235 atoms & 50 Lead-207 atoms, which is 1 times
After passage of 2 half-lives, we will have 25 Uranium-235 atoms & 75 Lead-207 atoms, which is 3 times
After passage of 3 half-lives, we will have 12.5 Uranium-235 atoms & 87.5 Lead-207 atoms, which is 7 times
After passage of 4 half-lives, we will have 6.25 Uranium-235 atoms & 93.75 Lead-207 atoms, which is 15 times
Hence, age of crystal can be determined to be between 2,130 (as per 3 half-lives) and 2,840 (as per 4 half-lives) million years old.
Answer (b)
Half-life of Uranium-238 to Lead-206 decay is 4.47 billion years.
With every passing 4.47 billion years, the number of Uranium atoms will be halved relative to the starting amount, and the same number of Lead atoms will be yielded.
After passage of 0 half-lives, we will have 100 Uranium-235 atoms & 0 Lead-207 atoms
After passage of 1 half-live, we will have 50 Uranium-235 atoms & 50 Lead-207 atoms, which is 50% of decay.
However, one half-life takes 4.47 billion years, and we have only 2.235 billion years.
Now 4.47 billion years produces 50% decay, therefore, on a linear scale,
2.235 billion years (half of one half-live) should produce 25% decay.
However decay is an exponentially decreasing scale/graph. (i.e. the rate of material loss decreases over time)
Hence we can deduce that more than 25% decay of Uranium-238 would have occured by the time 2.235 billion years have elapsed. ANSWER
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