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

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

Key Concepts

Exponential Decay Equation

The exponential decay equation, expressed as N = N0 exp(-?t), describes the decrease of a radioactive substance over time. This equation is fundamental in carbon dating as it relates the remaining quantity of the isotope to the time elapsed since the death of the organism.

Activity

Activity is the measure of the rate at which a radioactive sample decays, typically expressed in becquerels (Bq), which corresponds to one disintegration per second. It is directly proportional to the number of radioactive nuclei in the sample and is crucial for determining the time elapsed since the sample ceased exchanging with the environment.

Decay Constant

The decay constant is a parameter that quantifies the likelihood of a single atom decaying per unit time. It is mathematically related to the half-life, allowing for the calculation of elapsed time from the measured remaining activity in a sample.

Half-life

The half-life of a radioactive isotope is the time required for half of the original quantity of the substance to decay. It provides a measurable timescale for the decay process and is a critical parameter in computing the age of archaeological and geological samples.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. Over time, the number of undecayed nuclei decreases according to a predictable statistical law, forming the basis for methods used in age determination.

Carbon Dating

Carbon dating is a radiometric method that determines the age of formerly living organisms by measuring the amount of carbon-14 remaining in a sample. Since carbon-14 decays at a known rate after the organism's death, comparing its present concentration to the expected initial level provides an estimate of age.

Transcript

00:01 All right, question 81 states that a specimen taken from the wrappings of a mummy contains 7 .82 grams of carbon and has an activity of 1 .38 becaryl.

00:12 How old is the mummy? as a hint, or just a reminder, refer to section 323 for relevant information regarding the isotopes of carbon.

00:23 So these are our givens.

00:27 Because we're doing with something to do with carbon dating or dating in general using carbon, we know that the half -life of carbon 14 is 5 ,730 years.

00:37 That is in that section referred to in the book.

00:40 But i think more importantly for this question, in that book, it states the activity per gram of carbon 14.

00:48 The activity per gram, the initial activity per gram, because here we're given r, but we don't have an r -not.

00:58 We don't have an initial activity.

01:00 So if we multiply this rate to be 0 .21 becorel per gram, multiplied by our sample mass, 7 .82 grams, we are able to find that our initial activity for this carbon to be 1 .81 be 1 .81 becg.

01:34 So this is the most important part we got from that section 32 -3 to find r0.

01:41 So now that we have it, r not, we use the expression, the decay expression, e to the negative lambda t, solve for t to see how old our sample is.

01:56 So we can rearrange this equation, which we've done multiple times by now in the chapter and many of the questions.

02:02 To solve for the time, to be the natural algorithm, oh sorry, this expression is wrong.

02:10 It's r equals r not.

02:12 Aha, that should be, that should be obvious by now.

02:16 But i was removing...

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