The half-life of a sample has been defined as the time it takes for half of a sample to decay.The fifth-life can be defined as the time it takes for one-fifth of a sample to decay.Given these definitions,calculate the fifth-life of a sample that has a half-life of 26 years.
A)8.4 years
B)60 years
C)17 years
D)29 years
E)42 years

Question

Quizplus · Accepted Answer

The fifth-life can be calculated using the formula for exponential decay. If the half-life is 26 years, the decay constant λ is ln(2)/26. The fifth-life is the time t when 4/5 of the sample remains, so we solve 0.8 = e^(-λt) for t, which gives approximately 8.4 years.

The Half-Life of a Sample Has Been Defined as the Time