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?

Answer 1

a) A Helium nucleus with two protons and one neutron

b) 0.324 of the original amount

Step-by-step 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