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Standard XII

Physics

Half Life and Average Life

The fossil bo...

Question

The fossil bone has a $^{14} C :^{12} C$ ratio, which is $(\frac{1}{16})$ of that in a living animal bone. If the half of $^{14} C$ is $5730$ years, then the age of the fossil (in years) is :-

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Solution

Here $\frac{N}{N_{0}} = \frac{1}{16} = \frac{1}{2^{t / T_{h}}}$ (Here $T_{h} \to$ half life)
$\Rightarrow \frac{1}{2^{4}} = \frac{1}{2^{t / 5730}}$
$\Rightarrow t = 5730 \times 4 = 22920$ years.

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Similar questions

Q. The fossil bone has a

^{14} C :^{12} C

ratio, which is

[\frac{1}{16}]

of that in a living animal bone. If the half-life of

^{14} C

5730

years, then the age of the fossil bone is

Q. The fossil bone has a

^{14} C :^{12} C

ratio, which is

(\frac{1}{16})

of that in a living animal bone. If the half of

^{14} C

5730

years, then the age of the fossil (in years) is :-

The half-life for radioactive decay of ¹⁴C is 5730 years. An archaeological artifact containing wood had only 80% of the ¹⁴C found in a living tree. Estimate the age of the sample.

Q. A pieces of bone an animals from a ruin is found to have

^{14} C

activity of 12 disintegrations per minute per gm of its carbon content. The

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activity of of a living animal is 16 disintegration per minute per gm How long ago nearly did the animal die?
(Given half of life

^{14} C

t_{1 / 2}

=5760 years)

Q. The age of a sample of wood (in years), if only

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part of original

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The fossil bone has a 14C:12C ratio, which is (116) of that in a living animal bone. If the half of 14C is 5730 years, then the age of the fossil (in years) is :-

Here NN0=116=12t/Th (Here Th→ half life) ⇒124=12t/5730 ⇒t=5730×4=22920 years.

The fossil bone has a $^{14} C :^{12} C$ ratio, which is $(\frac{1}{16})$ of that in a living animal bone. If the half of $^{14} C$ is $5730$ years, then the age of the fossil (in years) is :-

Here $\frac{N}{N_{0}} = \frac{1}{16} = \frac{1}{2^{t / T_{h}}}$ (Here $T_{h} \to$ half life)
$\Rightarrow \frac{1}{2^{4}} = \frac{1}{2^{t / 5730}}$
$\Rightarrow t = 5730 \times 4 = 22920$ years.