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 1900 years old. Are they right ?

Answer 1

Answer:

The scroll is 1949 years old, thus the archeologists are right.

Step-by-step explanation:

The decay equation of ¹⁴C is:

$A = A_{0}e^{-\lambda*t}$   (1)

Where:

A₀: is the initial activity

A: is the activity after a time t = 79%*A₀

λ: is the decay rate

The decay rate is:

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

Where $t_{1/2}$: is the half-life of ¹⁴C = 5730 y

By entering equation (2) into equation (1) we can find the age of the scrolls.

$A = A_{0}e^{-\lambda*t} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}$

Since, A = 79%*A₀, we have:

$\frac{79}{100}A_{0} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}$

$ln(\frac{79}{100}) = -\frac{ln(2)}{t_{1/2}}*t$

Solving the above equation for t:

$t = -\frac{ln(79/100)}{\frac{ln(2)}{t_{1/2}}}$

$t = -\frac{ln(75/100)}{\frac{ln(2)}{5730 y}} = 1949 y$

Hence, the scroll is 1949 years old, thus the archeologists are right.

I hope it helps you!