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 freshlybottled specimen.

Answer 1

Answer: 29.0 years

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

`t_{(1)/(2)}=(0.693)/(k)`

`k=(0.693)/(12.5years)=0.0554years^(-1)`

b) for decomposition of 80 % of reactant

`t=(2.303)/(0.0554)\log(100)/(100-80)`

`t=(2.303)/(0.0554)\log(100)/(20)`

`t=29.0 years`

The age of a suspected vintage wine that is 20 % as radioactive as a freshlybottled specimen is 29.0 years