Question

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

Answer 1

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