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Difficulty: HardEvidence for Evolution: Paleontology and Fossil Records

A paleontologist analyzing a fossilized wood sample recovered from an undisturbed sedimentary rock layer determines that the sample contains 12.5%12.5\% of its original parent isotope, Carbon-14 (14C^{14}\text{C}). Given that the half-life of 14C^{14}\text{C} is 5,730 years5,730\text{ years}, what is the estimated absolute age of the fossil, and which principle distinguishes this method from relative dating?

  1. 17,190 years17,190\text{ years}; absolute dating determines numerical age in years using radioactive decay rates, whereas relative dating determines the chronological sequence of rock layers without providing specific ages.Answer
  2. B
    11,460 years11,460\text{ years}; absolute dating determines numerical age in years using radioactive decay rates, whereas relative dating measures the ratio of stable isotopes in index fossils.
  3. C
    17,190 years17,190\text{ years}; relative dating determines numerical age using index fossils, whereas absolute dating determines the vertical position of sedimentary strata.
  4. D
    22,920 years22,920\text{ years}; absolute dating determines the evolutionary order of fossil organisms, whereas relative dating calculates exact half-lives of unstable nuclei.

Answer

The estimated absolute age of the fossil is 17,190 years17,190\text{ years}. Absolute dating uses decay rates of radioisotopes to calculate specific numerical age, while relative dating determines sequential order of age based on rock strata position.
The option stating 17,190 years17,190\text{ years} with absolute dating measuring decay rates and relative dating determining sequential order is correct. The fraction of parent isotope remaining (12.5%=(1/2)312.5\% = (1/2)^3) indicates that exactly 3 half-lives have elapsed. Multiplying 3 by 5,730 years5,730\text{ years} yields 17,190 years17,190\text{ years}. Absolute dating uses radioisotope decay rates to estimate precise numerical age, while relative dating relies on stratigraphic principles to establish relative chronological sequence.

Step-by-Step Solution

1
Determine the number of half-lives that have elapsed from the given percentage of parent isotope.
After 1 half-life: 50%50\%; after 2 half-lives: 25%25\%; after 3 half-lives: 12.5%12.5\%. Thus, n=3n = 3 half-lives.
Radioactive decay follows an exponential decay process where the quantity of parent isotope is halved during each constant time interval (half-life).
2
Calculate the absolute age by multiplying the number of elapsed half-lives by the half-life duration of 14C^{14}\text{C}.
Age=3×5,730 years=17,190 years\text{Age} = 3 \times 5,730\text{ years} = 17,190\text{ years}.
The total elapsed time is the product of the number of half-lives and the duration of one half-life period.
3
Distinguish between absolute dating and relative dating principles.
Absolute dating (radiometric decay) gives a specific numerical age in years. Relative dating (law of superposition/index fossils) establishes only chronological order (older vs. younger).
Understanding the fundamental distinction between quantitative radio-isotopic measurements and qualitative stratigraphical comparison is key in paleontological evidence for evolution.

Key Concept

Radiometric Absolute Dating vs. Relative Stratigraphic Dating in Paleontology
Estimated Time:2m 0s
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Topics

Evidence for Evolution: Paleontology and Fossil Records

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