A specimen taken from the wrappings of a mummy contains 7.82 g of carbon and has an activity of

step 1 Problem number 81 The given is RC equal to 0 .231 BQ and Lwanda is equal to 1 .21 and lambda is

A specimen taken from the wrappings of a mummy contains 7.82...

A specimen taken from the wrappings of a mummy contains $7.82 \mathrm{g}$ of carbon and has an activity of $1.38 \mathrm{Bq} .$ How old is the mummy? (Refer to pages 1132 and 1133 for relevant information regarding the isotopes of carbon.)

Key Concepts

Radiocarbon Dating

Radiocarbon dating is a method used to determine the age of formerly living things by measuring the amount of carbon-14, a radioactive isotope of carbon, remaining in a sample. Since carbon-14 decays at a known rate after an organism dies, measuring its residual activity allows scientists to estimate the time elapsed since death.

Radioactive Decay Law

The radioactive decay law describes how the quantity of a radioactive isotope decreases over time exponentially, governed by its decay constant. This mathematical relationship is fundamental in dating techniques, where it relates the measured activity of a sample to its initial activity and the elapsed time.

Half-Life

The half-life of a radioactive isotope, such as carbon-14, is the period over which half of the original amount decays. In radiocarbon dating, the half-life (approximately 5730 years for carbon-14) is used to calculate the age of archaeological specimens by comparing the current level of radioactivity to the expected level in living organisms.

Activity Measurement

Activity measurement refers to determining the decay rate of a radioactive sample, typically expressed in becquerels (Bq). By comparing the measured activity of a specimen to the known activity of a modern reference, scientists can infer how much time has passed since the sample ceased exchanging carbon with the atmosphere.

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