Question

have The Shroud of Turin, which shows the negative image of the body of a man who appears to have been crucified, is believed by many to be the burial shroud of Jesus of Nazareth. In 1988 the Vatican granted permission to have the shroud carbon-dated. Three independent scientific laboratories analyzed the cloth and concluded that the shroud was approximately 660 years old,t an age consistent with its historical appearance. Using this age, determine what percentage of the original amount of C-14 remained in the cloth as of 1988. (The half-life of C-14 is approximately 5730 years. Round your answer to the nearest percent.) in the clothn

Answer 1

Answer:94%

Step-by-step explanation:

Half life of a radioactive element is the time taken for half it's mass to disintegrate away.it means after attaining half life,what will be left is 100-50=50%.

Let the 100% mass of C-14,be x

Then 5730years=1/2 of X

Then 660 years=y of X

Where Y is the fraction of C-14 that has disintegrate as at 1988.

5730/660=1/2X/yX

5730/660=1/2/y

Cross multiplying

5730×y=660×1/2

5730y=330

Y=330/5730=0.05759

In %,5.76%

Amount of C-14 left is

100-5.76=94.24=94% as at 1988.

Answer 2

Using an exponential equation, it is found that 92% of the original amount of C-14 remained in the cloth as of 1988.

An exponential equation for a decaying amount is given by:

$A(t) = A(0)e^{-kt}$

In which:

A(0) is the initial amount.

k is the decay rate, as a decimal.

The half-life of 5730 years means that when $t = 5730, A(t) = 0.5A(0)$, and this is used to find k. Hence:

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-5730k}$

$e^{-5730k} = 0.5$

$\ln{e^{-5730k}} = \ln{0.5}$

$-5730k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{5730}}$

$k = 0.00012096809$

Thus, the equation is:

$A(t) = A(0)e^{-0.00012096809t}$

The proportion remaining after 660 years is:

$A(660) = A(0)e^{-0.00012096809(660)}$

$A(660) = 0.92$

92% of the original amount of C-14 remained in the cloth as of 1988.

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