The nuclide ratio, `._(1)^(3) H` to `._(1)^(1) H` in a sample of water is `8.0xx10^(-18) : 1` Tritium undergoes decay with a half-life period of `12.3yr` How much tritium atoms would `10.0g` of such a sample contains `40` year after the original sample is collected?

Explanation

Mass of hydrogen in `1.0g` of water `=(2)/(18)xx10.0=1.111g`
Number of moles of `H` atoms in `10g` of water `=1.111 `
`:.` Number of atoms of `H` in `10` of water ltbr. `=1.111xx6.023xx10^(23)`
Number of atoms of `._(1)H^(3)` in `10.0g` of water
`=1.111xx6.023xx10^(23)xx(8.0xx10^9-18)/(1)`
`=5.3532xx10^(6)` ltbr `:'` Decay constant `(K)=(0.693)/(t_(1//2))` and
`K=(2.3030)/(t)"log"(N_(0))/(N)` ltbr. `:. (0.693)/(12.3)=(2.303)/(40)"log"([5.3532xx10^(6)])/(N_(t))`
`:. N_(t)=5.6223xx10^(5)`