# Radioactive Dating

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**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.

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**Radioactive
Dating**

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

** The atmosphere
contains radioactive carbon dioxide,

^{14}CO_{2}, and ordinary carbon dioxide,^{12}CO_{2}, 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,

^{14}C/^{12}C 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.

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**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

^{14}C/^{12}C 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^{14}C/^{12}C 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

^{12}C_{0}=^{12}C_{t}
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**

^{14}C/^{12}C**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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