Question:

The radioactive isotope to find the Earth's age in radiometric dating of rocks is

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  • To date very old materials like ancient rocks and the Earth, radioactive isotopes with very long half-lives are needed.
  • Uranium-238 (U-238) decays to Lead-206 (Pb-206) with a half-life of approx. 4.47 billion years. This is a primary method for dating the Earth.
  • Potassium-40 (K-40) decays to Argon-40 (Ar-40) with a half-life of approx. 1.25 billion years, also used for old rocks.
  • Carbon-14 has a much shorter half-life (5,730 years) and is used for dating relatively young organic materials.
  • Lead-206 is a stable daughter isotope, not the decaying parent.
Updated On: Jun 10, 2025
  • Carbon-14
  • Uranium-238
  • Potassium-40
  • Lead-206
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The Correct Option is B

Solution and Explanation

To determine the Earth's age using radiometric dating of rocks, the radioactive isotope commonly used is Uranium-238.

Step-by-Step Explanation:

Step 1: Understanding Radiometric Dating

Radiometric dating is a technique used to date materials based on the decay of radioactive isotopes. It relies on the principle that unstable (radioactive) parent isotopes decay into stable daughter isotopes at a predictable and constant rate, defined by their half-life. By measuring the ratio of the parent isotope to its daughter product in a sample, scientists can calculate the age of the material.

Step 2: Analyzing the Suitability of Each Isotope for Earth's Age

The Earth's age is estimated to be approximately 4.54 billion years. To date such an ancient object, a radioactive isotope with a very long half-life is required.

  • Carbon-14:
    • Half-life: Approximately 5,730 years.
    • Use: Primarily used for dating organic materials (once-living organisms) up to about 50,000 to 60,000 years old.
    • Suitability for Earth's Age: Its half-life is far too short to date the Earth, which is billions of years old.
  • Uranium-238:
    • Half-life: Approximately 4.468 billion years.
    • Decay product: Decays through a series of steps to stable Lead-206.
    • Use: The Uranium-Lead (U-Pb) dating method, utilizing both Uranium-238 (to Lead-206) and Uranium-235 (to Lead-207), is considered one of the most reliable and precise dating methods for very old geological materials, including the oldest rocks on Earth and meteorites (which are used to estimate the Earth's formation age). Its half-life is perfectly suited for dating events on a multi-billion-year scale.
    • Suitability for Earth's Age: Highly suitable.
  • Potassium-40:
    • Half-life: Approximately 1.251 billion years.
    • Decay product: Decays to Argon-40 (and Calcium-40).
    • Use: The Potassium-Argon (K-Ar) dating method is widely used for dating rocks, particularly volcanic and metamorphic rocks, with ages ranging from a few thousand to billions of years. While capable of dating ancient rocks, the U-Pb system is often preferred for determining the absolute age of the Earth due to its longer half-life and independent decay chains that provide internal cross-checks.
    • Suitability for Earth's Age: Potentially suitable for very old rocks, but Uranium-238 is more directly associated with the precise determination of the Earth's primordial age.
  • Lead-206:
    • Nature: Lead-206 is a stable *daughter product* of Uranium-238 decay.
    • Use: Its presence and ratio to its parent Uranium-238 are measured to determine the age. It is not the radioactive isotope itself that decays.
    • Suitability for Earth's Age: It is part of the dating system, but not the radioactive "parent" isotope being sought by the question.

Step 3: Conclusion

For dating objects as old as the Earth, an isotope with a half-life comparable to or longer than the Earth's age is essential. Among the choices provided, Uranium-238 has a half-life (4.468 billion years) that makes it ideal for this purpose, and it is indeed a primary isotope used in the highly accurate Uranium-Lead dating method to determine the age of the Earth and the early solar system.

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