Question

Question #bbfad

Answer 1

After 49 years you'll have `5 * 10^(-19)` tritium atoms for every normal hydrogen atom present in the sample.

What you've essentially have to perform is a nuclear half-life calculation starting from the initial ratio of tritium to hydrogen atoms.

In tritium's case, the total number of atoms will be reduced to half after every half-life; this means that you'll have half of the number of tritium atoms after 12.3 years, a quarter of the initial tritium atoms after 2 * 12.3 = 24.6 years, and so on.

Since normal hydrogen is considered stable, i.e. it has a half-life that's bigger than the age of the universe (by a lot), the number of hydrogen atoms will remain the same.

You can use the nuclear half-life equation to see how many tritium atoms you'll have after 49 years

`A(t) = A_0 * (1/2)^(t/t_("1/2"))` (1), where

`A(t)` - the amount left after t years;
`A_0` - the initial quantity of the substance that will undergo decay;
`t_("1/2")` - the half-life of the decaying quantity.

So, plug your data into this equation and solve for `A(t)`

`A(t) = 8 * 10^(-18)"atoms" * (1/2)^(("49 years")/"12.3 years")`

`A(t) = 0.5056 * 10^(-18)"atoms" = 5.06 * 10^(-19)"atoms"`

Rounded to 1 sig fig, the number of sig figs in `8 * 10^(-18)`, the ratio will now be `5 * 10^(-19)` tritium atoms for every hydrogen atom.