A skull believed to belong to an ancient human being has a carbon-14 decay rate of 4.50 disintegrations per minute per gram of carbon (4.50 dis/min · g C). If living organisms have a decay rate of 15.3 dis/min · g C, how old is the skull? (The decay rate is directly proportional to the amount of carbon-14 present.)

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SORT You are given the current rate of decay for the skull and the assumed initial rate. You are asked to find the age of the skull, which is the time that passed in order for the rate to have reached its current value. STRATEGIZE Use the expression for half-life (Equation 21.1) to find the rate constant (k) from the half-life for C-14, which is 5715 years (Table 21.3). GIVEN: rate, = 4.50 dis/min .g C; rate = 15.3 dis/min . g C; FIND: t CONCEPTUAL PLAN 11/2 t1/2 = 0.693 k k