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

Answer:

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

Step-by-step 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:

$\lambda = \frac{ln(2)}{t_{1/2}}$   (2)    

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

$t = \frac{t_{1/2}*ln(N_{t}/N_{0})}{ln(2)} = \frac{5730*ln(0.79)}{ln(2)} = 1948.6 y$

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!