Question

A fossil is found to have $ \dfrac{1}{32} $ of its carbon $ -14 $ remaining. How old is the fossil?

Answer 1

Hint :For any item that gives proof of a past life type that has been preserved in the crust of the Earth, the word fossil is a broad term. Fossils may consist of imprints in sedimentary rock, petrified remains, or even an entire specimen conserved in amber, ice or tar. Although most fossils contain some quantity of the element carbon, a special form known as a carbon.

Complete Step By Step Answer:
All living organisms contain carbon, and an incredibly thin layer of carbon is accumulated over time on the rock when a dead organism lies on a rock. Since the hydrogen, oxygen and nitrogen in the body of the organism normally vanish when dissolved and vaporized under a body of water, this layer of carbon is the only remaining substance. Carbonization or distillation is called this decaying process.
Carbon films fossils are created from a soft-bodied organism's carbon residue that has been buried in sediment. Most of the body is constructed from carbon, or some organism. It may become coated in layers of sediment when an organism dies. Eventually, all the materials that make up the dead organism's body break down from the heat and the immense weight of the sediment's overlying layers, leaving nothing but carbon.
After the more volatile oxygen, nitrogen, and hydrogen dissolve, the stable carbon in the body of the organism remains. A thin layer or residue of carbon in the form of the body's outline is what is left.
Here we have $ \dfrac{1}{32} $ fossils of life, and we know that it can re-written as $ {{2}^{5}}=32 $
Therefore, $ \dfrac{1}{32}=\dfrac{1}{{{2}^{5}}} $ so the fossil has aged for 5 half-lives.
Assuming the half-life is $ 5,730~ $ years, that's $ 5\times 7,730=28,650 $ years old.

Note :
In tandem with compression fossils, carbon film fossils sometimes occur, and the combination often increases the likelihood of collecting more data than the general shape and morphology of the organism that created the fossil. Internal leaf elements, such as cell walls and internal cell structures, are typically lost in the case of leaves, but cells are often.