A sample of a dish from an archaeological dig gave 18 500 disintegrations per gram of carbon per day.A 1.00-g sample of carbon from a modern source gave 22 080 disintegrations per day.If the decay constant of carbon-14 is 1.2 * 10^-4 y^-1,what is the age of the dish?

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Quizplus · Accepted Answer

The age of the dish can be calculated using the formula:$$t = \frac{1}{\lambda} \ln \frac{A_0}{A}$$where:* t is the age of the dish* λ is the decay constant of carbon-14* A_0 is the initial activity of the carbon-14 sample* A is the activity of the carbon-14 sample at time tIn this case, we have:* A_0 = 22 080 disintegrations per day* A = 18 500 disintegrations per day* λ = 1.2 * 10^-4 y^-1Substituting these values into the formula, we get:$$t = \frac{1}{1.2 * 10^-4 y^-1} \ln \frac{22 080 disintegrations per day}{18 500 disintegrations per day}$$$$t = 8300 y$$Therefore, the age of the dish is 8300 years.

A Sample of a Dish from an Archaeological Dig Gave