The radioactive hydrogen isotope 3H is called tritium. It decays by beta-minus decay with a half-life of 12.3 years. A. What is the d

Question

The radioactive hydrogen isotope 3H is called tritium. It decays by beta-minus decay with a half-life of 12.3 years.
A. What is the daughter nucleus of tritium?
B. A watch uses the decay of tritium to energize its glowing dial. What fraction of the tritium remains 20 years after the watch was created?

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Ngọc Hoa 4 years 2021-08-04T00:59:11+00:00 1 Answers 104 views 0

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  1. yenoanh
    0
    2021-08-04T01:00:19+00:00
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    Answer:

    a) A Helium nucleus with two protons and one neutron

    b) 0.324 of the original amount

    Explanation:

    a) When Tritium decays, the nucleus emits an electron and an antineutrino, which then changes it from a Triton with one proton and two neutrons, to a Helium nucleus with two protons and one neutron.

    The decay constant for the decay of Tritium is gotten from

    t_{1/2} = 0.693/k

    where

    t_{1/2} is the half life = 12.3 yrs

    k is the decay constant = ?

    substituting, we have

    12.3 = 0.693/k

    k = 0.693/12.3 = 0.0563

    The fraction that will remain after 20 years can be calculated from

    N = N_{0} e^{-kt}

    where

    N is the final remaining amount of Tritium after 20 years

    N_{0} is the original amount of Tritium

    k is the decay constant = 0.0563

    t is the time = 20 years

    Equation can be re-written as

    N/N_{0} = e^{-kt}

    where

    N/N_{0} is the fraction of the tritium that will be remaining after 20 years.

    substituting values, we have

    N/N_{0} = e^{-0.0563 * 20}

    N/N_{0}  =  e^{-1.126}

    N/N_{0} = 0.324 of the original amount

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