Question

How many years will it take for 88.0 grams of tritium to decay to an 11.0 gram sample? (The half-life of tritium is 12.3 years.)

Answer 1

Radioactive decay exhibits first order kinetics. Let's derive the rate constant,

`t_(1/2) = ln(2)/k`

`12.3y = ln(2)/k => k approx 5.64*10^-2y^-1`,

and solve for the time it takes to decay. Recall,

`ln[A]_t = -kt + ln[A]_0`

`=> t = -ln(([A]_t)/([A]_0))/k`

Hence,

`t = -ln((11.0g)/(88.0g))/(5.64*10^-2y^-1) approx 36.9y`

is the time it takes for tritium to decay to the mass in your data.

Notice: I treat the mass of the radioactive nuclide as concentration to make calculation easier.