The age of water or wine may be determin ed by measuring its radioactive tritium

Question

The age of water or wine may be determin ed by measuring its radioactive tritium (3 1 H) content. Tritium, present in a steady state in nature, is formed primarily by cosmic irradiation of water vapor in the upper atmosphere, and it decays spontaneously by a first -order process with a half-life of 12.5 years. The formation reaction does not occur significantly inside a glass bottle at the surface of Earth. Enter the age in years of a suspected vintage wine that is 20% as radioactive as a freshly bottled specimen. Do not enter the units and use two significant figures.

Explanation / Answer

20% left.. so

A0 = 100%

A = 20%

then

apply half life equation

A = A0*(1/2)^(t/HL)

solve for t

since HL = 12.5 years

then

20% = 100% * (1/2)^(t/12.5)

0.2 = (1/2)^(t/12.5)

ln(0.2)/(ln0.5) = t/12.5

t = 12.5*ln(0.2)/(ln0.5)

t = 29.024 years -- >2 sig fig, 29 years

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.