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Chapter 5: Q.5.55 (page 164)

Carbon dating of small bits of charcoal used in cave paintings has determined that some of the paintings are from 10000 to 30000 yr old. Carbon- 14 has a half-life of 5730 yr. In a 1-渭gsample of carbon from a live tree, the activity of carbon-14 is 6.4 渭Ci. If researchers determine that 1 渭gof charcoal from a prehistoric cave painting in France has an activity of 0.80渭Ci, what is the age of the painting?

Short Answer

Expert verified

The age of the painting is17188.6years.

Step by step solution

01

Part (a) Step 1: Given Information

Carbon-14has a half-life of5730yr.

In a 1渭g-sample of carbon from a live tree, the activity of carbon-14isrole="math" localid="1653888138969" 6.4渭Ci

1 渭gof charcoal from a prehistoric cave painting in France has an activity of 0.80渭Ci.

Finding the age of the painting.

02

Explanation

The half-life of Carbon-14 =t12=5730years

The activity of carbon-14 =伪o=6.4渭Cidecay/secand the activity of painting =伪t=0.8渭Cidecay/sec

Using the formula,

localid="1653888609726" t12=0.693位鈬�位=0.693t12=0.6935730=1.21脳10-4decay

t=鈭�1位ln鈦�伪t伪olocalid="1653888756897" 鈬�t=鈭�11.21脳10鈭�4脳2.303脳log鈦�0.86.4=17188.6yrs

Hence the age of the painting is t =171886.6years

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a) The dosage of technetium-99mfor a lung scan is 20. 渭CM/kgof body mass. How many millicuries of technetium-99m should be given to a50.0-kg person (1mCi=1000渭Ci)?

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