# Carbon Dating and Geiger Muller Tube

Carbon dating:

The process of estimating the time of death of an animal from its fossil is known as carbon dating. The neutrons produced due to cosmic radiation react with N-14 to give C-14 isotope.

0n1 + 7N14  → 6C14 + 1H1

The C-14 isotope thus produced is radioactive and emits β-particles as

6C14  → 7N14 + -1e0

The process continues and the amount of C14 available in the environment is maintained at equilibrium. Its ratio to the C-12 isotope is 1:1012 and is same for carbon available in animal’s body as long as it is alive. As the animal dies further intake of carbon stops. The C-14 of its fossil starts to decay (β-decay) and the rate of emission also decrease. If R0 is the rate of decay when the animal is alive and R is the rate of decay of fossil then, from the law of radioactive disintegration,

$$R = R_oe^{-\lambda t}$$
$$or, e^{-\lambda t} = \frac{R}{R_o}$$
$$or, \lambda t =log_e\frac{R}{R_o}$$
$$\therefore t=\frac{1}{{\lambda}}log_e\frac{R}{R_o}$$

The half life of C-14 is 5730 years.

Geiger Muller tube

Geiger Muller Tube

Geiger Muller tube is a device that is used to count the rate of radioactive decay.

It consists of a glass tube coated inside with metal. A metallic rod is inserted at its axis. A high voltage is supplied between the tube and the axis rod. The pressure inside the tube is about 10 mm of Hg. At this condition the tube is almost ready to discharge. The disturbance created by α or β particles coming from radioactive source produces an avalanche of electrons inside the tube and high current is set up in the circuit which passed through a counter displays the rate of decay. In this way the rate of radioactive decay is measured.

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