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Radioactive Dating



Radioactivity


** A number of elements such as uranium and radium are unstable. Their atomic nucleus breaks of its own accord to form a smaller atomic nucleus of another element. The protons and neutrons in the unstable nucleus regroup to give the new nucleus. This causes the release of excess particles and energy from the original nucleus, which we call radiation.

** The elements whose atomic nucleus emits radiation are said to be radioactive.

Radioactive Dating


** The age of an old piece of wood can be determined by radioactive dating technique.

** The atmosphere contains radioactive carbon dioxide, 14CO2, and ordinary carbon dioxide, 12CO2, in a fixed ratio.

** A plant while alive takes up both types of carbon dioxide and converts them to carbon-14 and carbon-12 photosynthesis.

** Thus a living plant contains radioactive carbon-14 and stable carbon-12 in a fixed ratio. When the plant dies, the uptake of carbon from the atmosphere stops.

** Now onward, carbon-12 remains unchanged but carbon-14 decays by beta emission.


As a result, 14C/ 12C decreases with lapse of time.

** Therefore the concentration of carbon-14 declines with time.

** The concentration of carbon-14 can be measured by counting radioactivity.

** Knowing the concentration of carbon-14 in a given sample of old wood and that in a living plant, the age of the sample can be calculated.

Solved Problem


Problem(1): The amount of carbon-14 in a piece of wood is found to be one-sixth of its amount in a fresh piece of wood. Calculate the age of old piece of wood.

Solution:

Calculation of Decay constant :

The half-life of carbon-14 = 5730 years


Calculation of Age of Wood :



** In a new method for determining the age of old wood (or fossil) the measurement of radioactivity is avoided.

** The ratio 14C/12C is found with the help of a mass spectrometer in the old wood and fresh wood from a living plant. It is assumed that the ratio 14C/12C in the fresh wood today is the same as it was at the time of death of the plant.

** Let the ratio in the fresh plant at t = 0 be


Let the ratio in the old piece of wood at time t be


Dividing (1) by (2):


The concentration of carbon-12 does not change with time and 12C0 = 12Ct

Therefore

where the ratio in the old wood is y/x times the ratio in the living plant.

Knowing the value of y/x, the value of t can be found from the expression:



Problem (2): A bone taken from a garbage pile buried under a hill-side had 14C/12 ratio 0.477 times the ratio in a living plant or animal. What was the date when the animal was buried?

Solution:

Half-life of carbon-14 is 5730 years


Substituting values in the expression


The animal was buried 6100 years ago.

Reference: Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.



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