The interesting application of beta decay is radioactive dating or carbon dating.

**Carbon dating**

The interesting application of beta
decay is radioactive dating or carbon dating. Using this technique, the age of
an ancient object can be calculated. All living organisms absorb carbon dioxide
(CO_{2}) from air to synthesize organic molecules. In this absorbed CO_{2},
the major part is ^{12}_{6}*C
*and very small fraction (1.3 Ã—10^{-12} ) is radioactive ^{14}_{6}*C *whose half-life is 5730 years.

Carbon-14 in the atmosphere is
always decaying but at the same time, cosmic rays from outer space are
continuously bombarding the atoms in the atmosphere which produces ^{14}_{6}*C *. So the continuous production and decay
of ^{14}_{6}*C *in the atmosphere
keep the ratio of ^{14}* _{6}C
*to

** **

Keezhadi (à®•à¯€à®´à®Ÿà®¿), a small hamlet, has become one of the very important archeological
places of Tamilandu. It is located in Sivagangai district. A lot of tools, jewellery
and charcoal, etc.) have been unearthed in Keezhadi which have given
substantial evidence that an ancient urban civilization had thrived on the
banks of river Vaigai. To determine the age of those
materials, the charcoal of 200 g sent for carbon dating is given in the
following figure (b). The activity of ^{14}_{6}*C *is found to be 38 decays/s. Calculate
the age of charcoal.

To calculate the age, we need to
know the initial activity (R_{0}) of the characol (when the sample was
alive).

The activity R of
the sample

*R *= *R _{0} e*

To find the time *t*, rewriting the above equation (1), *e*^{Î»t}* *= *R*_{0}/R

By taking the logarithm on both sides, we get

Here *R *= 38 decays/s=38 Bq.

To find decay constant, we use the equation

[âˆ´ 1yr =
365.25 Ã— 24 Ã— 60 Ã— 60 s = 3.156 Ã— 10^{7} s]

Î» = 3.83Ã—10^{âˆ’12}
*s*^{âˆ’1}

To find the initial activity *R*_{0}, we use the equation *R*_{0} = Î»*N*_{0} . Here *N*_{0}
is the number of carbon-14 atoms present in the sample when it was alive. The
mass of the characol is 200 g. In 12 g of carbon, there are 6.02 Ã—10^{23 }carbon
atoms. So 200 g contains,^{}

[{ 6.02Ã—10^{23} atoms / *mol *} / {12*g */ *mol* } ] Ã— 200 â‰ˆ 1Ã—10^{25}* *Atoms

When the tree(sample) was alive, the
ratio of ^{14}_{6}*C *to
^{12}_{6}*C *is 1.3 Ã—10^{-12}
. So the total number of carbon-14 atoms is given by

*N _{0} *= 1Ã—10

The initial activity

*R _{0} *= 3.83Ã—10

= 50 *Bq*

By substituting the value of *R*_{0} and Î» in the equation (2),
we get

In fact, the excavated materials
were sent for carbon dating to USA by Archeological Department of Tamilnadu and
the report confirmed that the age of Keezhadi artefacts lies between 2200 years
to 2500 years (Sangam era- 400 BC to 200 BC). The Keezhadi excavations
experimentally proved that urban civilization existed in Tamil Nadu even 2000
years ago!

Tags : Radioactivity | Nuclear Physics , 12th Physics : UNIT 9 : Atomic and Nuclear Physics

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12th Physics : UNIT 9 : Atomic and Nuclear Physics : Carbon dating | Radioactivity | Nuclear Physics

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