Chapter 6: Q65P (page 1478)

A bone fragment found in a cave believed to have been inhabited by early humans contains 0.29 times as much ${}^{14}C$ as an equal amount of carbon in the atmosphere when the organism containing the bone died. (See Example 43.9 in Section 43.4.) Find the approximate age of the fragment.

Short Answer

Expert verified

The approximate age of the fragment is 10233 years.

Step by step solution

Known information

The number N of remaining nuclei after time t is given by:

$N = N_{0} e^{- λt}$ ............... (i)

Where $N_{0}$ is the number of nuclei at t = 0.

The relation between the half-life $T_{1 / 2}$ and the decay constant $λ$ is given by:

$λ = \frac{In 2}{T_{1 / 2}}$ ................(ii)

Calculation of the approximate age of the fragment

Since the bone fragment contains0.29 times as much ${}^{14}C$ as an equal amount of carbon in the atmosphere when the organism containing the bone died, then we have $N / N_{0} = 0.29$ .

$N / N_{0} = 0.29 = e^{- λ t} e^{λ t} = 3.45 t = \frac{I n 3.45}{λ}$

Now, we substitute for $λ$ from equation (ii), so we get:

$t = \frac{T_{1 / 2} I n 3.45}{I n 2} = 1.79 T_{1 / 2}$

Finally, we plug our value of $T_{1 / 2} = 5730 y e a r s$ for ${}^{14}C$ , so we get the time it takes for ${}^{14}C$ an atom to reach this fraction:

$t = 1.79 \times (5730 y e a r s) = 10233 y e a r s$

Thus, the approximate age of the fragment is 10233 years.

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A bone fragment found in a cave believed to have been inhabited by early humans contains 0.29 times as much ${}^{14}C$ as an equal amount of carbon in the atmosphere when the organism containing the bone died. (See Example 43.9 in Section 43.4.) Find the approximate age of the fragment.

Short Answer

Step by step solution

Known information

Calculation of the approximate age of the fragment

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A bone fragment found in a cave believed to have been inhabited by early humans contains 0.29 times as much C14as an equal amount of carbon in the atmosphere when the organism containing the bone died. (See Example 43.9 in Section 43.4.) Find the approximate age of the fragment.

Short Answer

Step by step solution

Known information

Calculation of the approximate age of the fragment

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Electromagnetism

Work Energy and Power

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Physics of Motion

Engineering Physics

Study anywhere. Anytime. Across all devices.

A bone fragment found in a cave believed to have been inhabited by early humans contains 0.29 times as much ${}^{14}C$ as an equal amount of carbon in the atmosphere when the organism containing the bone died. (See Example 43.9 in Section 43.4.) Find the approximate age of the fragment.