Tritium (half-life = 12.3 yr) is used to verify the age of expensive brandies. If an old brandy contains only 1/64 of the tritium present in new brandy, then how long ago (in yr) was it produced?
We can use the formula for radioactive decay to solve this problem:
N(t) = N0*(1/2)^(t/T)
Where:
N(t) = final amount of tritium present in the old brandy (1/64 of the initial amount)
N0 = initial amount of tritium present in the new brandy
t = time in years that has passed
T = half-life of tritium (12.3 years)
Given that the old brandy contains 1/64 of the tritium present in the new brandy, we can write:
1/64 = (1/2)^(t/12.3)
Taking the log of both sides:
log(1/64) = log((1/2)^(t/12.3))
log(1/64) = (t/12.3) * log(1/2)
log(1/64) = -6 = t/12.3 * -0.3010
t = -6 / -0.3010 = 19.93
Therefore, the old brandy was produced approximately 19.93 years ago.