Question

Between the years of 1947 and 1956, earthenware jars containing what are known as the Dead Sea Scrolls were found in caves along the coast of

Jerusalem in the Dead Sea. Upon radiometric testing, it was found that the scrolls were wrapped in material that contained about 79 percent of

the original carbon-14. Archeologists estimated that the scrolls are about 1,900 years old. Are they right?

Question 1

Using the half-life of carbon-14 (5,730 years), prove or disprove this estimate age. Describe how you are testing this hypothesis.

Answer 1

Explanation:

Using the half-life equation, At = Ao (1 / 2) ^ t / h, the number of years (1,900) can be substituted for t and the half-life (5,730) can be substituted for h. Since the original amount is unknown but the remaining percent is known, any value can be used for the original amount. Using 100 will be the easiest. Plugging these values into the equation gives At=100 (1 / 2) ^1900 / 5730=79.47 remaining. If 79.47 of the original 100 units are left, that is 79.47 percent. Since radiometric dating estimates age, the archeologists’ hypothesis is correct.

Answer 2

They are right, the time calculated using the exponential decay equation is 1948.6 years.

Explanation:

The time can be calculated using the exponential decay equation:

`N_((t)) = N_(0)e^(-\lambda t)` (1)

Where:

N(t): is the quantity of C-14 at time t

N₀: is the initial quantity of C-14

λ: is the decay constant

The decay constant is:

`\lambda = (ln(2))/(t_(1/2))` (2)

By entering equation (2) into (1) and solving for t, we have:

`t = (t_(1/2)*ln(N_(t)/N_(0)))/(ln(2)) = (5730*ln(0.79))/(ln(2)) = 1948.6 y`

Therefore, the time of the scrolls estimated by the archeologists is right, since the time calculated using the exponential decay equation is 1948.6 years.

I hope it helps you!