A researcher claims that an ancient scroll originated from greek scholars in about 500 bce. a measure of its carbon-14 decay rate gives a value that is 89% of that found in living organisms. how old is the scroll? (the half-life of carbon-14 is 5730 yr.) express the time in years as an integer.

Question

Chemistry

Greene

2 March, 20:17

A researcher claims that an ancient scroll originated from greek scholars in about 500 bce. a measure of its carbon-14 decay rate gives a value that is 89% of that found in living organisms. how old is the scroll? (the half-life of carbon-14 is 5730 yr.) express the time in years as an integer.

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Karlie Marks · Answer 1

The amount of substance present in a certain object with a given half-life in terms of h can be expressed through the equation,

A (t) = (A (o)) (0.5) ^ (t/h)

where A (t) is the amount of substance after t years and A (o) is the original amount. In this item we are given that A (t) / A (o) is equal to 0.89. Substituting the known values,

0.89 = (0.5) (t / 5730 years)

The value of t from the equation is 963.34 years.

Answer: 963 years