Question

A radioactive nucleus has a half-life of 5 x 108 years. Assuming that a sample of rock (say, in an asteroid) solidified right after the solar system formed, approximately what fraction of the radioactive element should be left in the rock today?

Answers

  1. Answer:

    So the present mass will be 0.0017002 times of the initial mass of the sample.

    Explanation:

    Given:

    • half life of the given sample, t'=5\times 10^8\ yrs
    • We know that solar system came in to existence approximately 4.6\times 10^{9} years ago.

    Let the initial quantity on the formation of the solar system be, m_o

    Then the final quantity at present be:

    m=m_o\times (\frac{1}{2})^{(t/t')}

    m=m_o\times (\frac{1}{2} )^{4.6\times 10^9\div(5\times 10^8)}

    m=m_o\times 0.0017002

    So the present mass will be 0.0017002 times of the initial mass of the sample.

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