# Question bbfad

Mar 8, 2015

After 49 years you'll have $5 \cdot {10}^{- 19}$ 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

$A \left(t\right) = {A}_{0} \cdot {\left(\frac{1}{2}\right)}^{\frac{t}{t} _ \left(\text{1/2}\right)}$ (1), where

$A \left(t\right)$ - the amount left after t years;
${A}_{0}$ - the initial quantity of the substance that will undergo decay;
${t}_{\text{1/2}}$ - the half-life of the decaying quantity.

So, plug your data into this equation and solve for $A \left(t\right)$

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

$A \left(t\right) = 0.5056 \cdot {10}^{- 18} \text{atoms" = 5.06 * 10^(-19)"atoms}$

Rounded to 1 sig fig, the number of sig figs in $8 \cdot {10}^{- 18}$, the ratio will now be $5 \cdot {10}^{- 19}$ tritium atoms for every hydrogen atom.