Suppose that you measure the intensity of radiation from carbon-14 in an ancient piece of wood to be 6% of what it would be in a freshly cut piece of wood. show that the age of this artifact is 23,000 years old.

t = 23136 years old

Explanation:

The intensity of radiation obeys the exponential decay law.

(1)

Here:

λ is the radiation decay constant.

I is the intensity of radiation after t time.

I₀ is the initial  intensity of radiation.

t is the time

Now, we know that the intensity of radiation is a 6% of what it would be in a freshly cut piece of wood, in other words:

(2)

Combining (2) with (1), we have:

(3)

Now, we just need to solve (3) for t.

(4)

and (5)

is the half-life.

In our case, we have ¹⁴C, so the

Finally, we can find t putting (5) in (4):

I hope it helps you!

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