Question

The age of water or wine may be determined by measuring its radioactive tritium(3H) content. Tritium, present in a steady state in nature, is formed primarily by cosmicirradiation of water vapor in the upper atmosphere, and it decays spontaneously by a firstorder process with a half-life of 12.5 years. The formation reaction does not occursignificantly inside a glass bottle at the surface of the earth.

Calculate the age of a suspected vintage wine that is 20% as radioactive as a freshly bottled specimen. Radioactivity follows first order rate kinetics.

Answer 1

Age of wine is 29 years

Step-by-step explanation:

The rate of decay of a radioactive isotope obeys the following formula:

`Ln (N)/(N_0) =-Kt` (1)

Where N is moles of atoms in time t, N₀ is initial moles of atoms, K is decay constant and t is time.

It is possible to obtain decay constant, K, from half-life, thus:

`t_(1/2) = (ln2)/(K)`

12.5 years = ln 2 / K

K = 0.05545 years⁻¹

If the wine is 20% as radioactive, N/N₀ = 0.2 / 1 = 0.2. The initial moles of atoms in percent is 100% = 1.

Replacing these values in (1):

`Ln {0.2} = -0.05545years^(-1)t`

29 years = t

Thus, age of wine is 29 years