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
[tex]t_{1/2}[/tex] = 0.693/k
where
[tex]t_{1/2}[/tex] 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
[tex]N[/tex] = [tex]N_{0} e^{-kt}[/tex]
where
[tex]N[/tex] is the final remaining amount of Tritium after 20 years
[tex]N_{0}[/tex] 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
[tex]N/N_{0}[/tex] = [tex]e^{-kt}[/tex]
where
[tex]N/N_{0}[/tex] is the fraction of the tritium that will be remaining after 20 years.
substituting values, we have
[tex]N/N_{0}[/tex] = [tex]e^{-0.0563 * 20}[/tex]
[tex]N/N_{0}[/tex] = [tex]e^{-1.126}[/tex]
[tex]N/N_{0}[/tex] = 0.324 of the original amount
