## Geiger Muller Tube and Radio Carbon Dating

Subject: Physics

#### Overview

The isotopes of an element which are also radioactive are called radioactive isotopes or simply radioisotopes.This note provides us an information on Geiger Muller tube and radio carbon dating.

#### Geiger-Muller Tube

A Geiger-Muller (GM) tube is a device used to detect ionizing articles or nuclear radiation. It consists of a glass cylinder G coated with a metal inside it as cathode C. A metal wire runs along the axis of the cylinder as anode A. as shown in the figure. The cylinder is filled with a gas such as argon mixed with halogen vapour at a low pressure of about 10 cm of Hg. The tube has very thin mica end window W shielded by a protective gauge P.

The high tension source (H.T.) supplies a potential difference of value little less than the ionizing potential of the gas through the resistance R. when a single ionizing particle, like a β particle or a γ-ray photon, enter the tube, through the window W, it will produce the ionization of the gas. The potential applied accelerates the ions towards the electrodes which produce more ions making collisions with gas molecules. So, an avalanche of ions is produced inside the tube which rushes towards the electrodes and produces a current in external resistance R. The resulting drop in potential across R reduces the potential across the tube below the threshold value and the decays rapidly as the circuits have a small time constant. This momentary surge of current produces an electric pulse which corresponds to one particle entering the counter. The successive current pulse generated in the resistance R, corresponding to the number of ionization particles passing into the tube, are detected and counted by a suitable arrangement.

The radioactive particles emitted from a given sample in a given interval of time can be counted by placing the sample at some distance from the window.

The isotopes of an element which are also radioactive are called radioactive isotopes or simply radioisotopes. For example, C14, C12 C11 are the isotopes of carbon. As C14 and C11 emit radioactive radiation, they are known as radioisotopes of carbon. Similarly, Na23, Na24 are the radioisotopes of sodium.

Nuclear radiations are widely used in medicine and therapy.

1. Diagnosis
1. Radioiodine I131 is used to determine the condition of the human thyroid gland.
2. Radio sodium (Na24) is used to locate the place of construction, restricting blood circulation in a patient.
3. Radio chromium (Cr51) is used to locate the exact position where hemorrhage might have taken place inside the body.
4. Water contents of the body are measured by using deuterium and tritium as the tracer.
5. Ga67 is used in tumour localization.
6. Tc99 is used in locating cancers, embolism, and other pathologies.
2. Therapy
1. Gamma radiations emitted by radiocobalt (Co60) are used destroy concerns tumors in the body.
2. Radio gold (Au198) and radiocobalt are used in a treatment of some cancer.
3. Radio phosphorous (p32) is used for treating skin diseases and leukemia.
4. Radio bismuth is use in the treatment of syphilis.
5. Radioiodine is used to treat an overactive thyroid gland.
3. Gamma radiations from cobalt-60 are used in hospitals for sterilization of materials like dressing, hypodermic syringes, and surgical sutures. Heat sensitive instruments and materials are sterilized by gamma radiations.
1. Many radiations from cobalt-60 are used for industrial radiography i.e. for investing the interiors of metallic castings for detecting any flaws or defects.
2. Radioactive radiations are used in the production and modification of plastic.
3. Nuclear radiations like γ-rays have been utilized for a preservation of food.
4. Radiation mutation in plants has been practiced to produce new varieties of these plants.
5. Radioactive iron can be used to study piston ring were.
6. The effectiveness of detergent products is tested using radioactive dirt.
##### Nuclear Reaction

The reaction involving the change in the structure of nucleus itself is called nuclear reaction. The first artificial nuclear reaction was produced by Rutherford in 1919. The reaction is

$$_2He^4 + _7N^{!4} \rightarrow _8O^{17} + _1 H^1$$

In this reaction 2He4 is bombarding particle, 7N17 is target nucleus, 1H1 is product particle and 8O17 is product nucleus. The reaction can be written as $\alpha (N^{14}, O^{17} ) P$. In all nuclear reaction, conservation principle for a charge, momentum, angular momentum, mass-energy, mass number etc are obeyed.

The process of dating an ancient object by measuring the proportion of 6C14 to 6C12 in a specimen is called carbon dating.

The atmosphere contains carbon 6C12 and its radioisotopes 6C14. Neutron produced by cosmic rays reacts with nitrogen in air to form 6C14 as below:

$$_7N^{14} + _0n^1 \rightarrow _6C^{14} + _1 H^1$$

The ratio 6C14 to 6C12 in the atmosphere is about 10-12. Both 6C14 to 6C12 combine with oxygen to form carbon dioxide that is absorbed by the living plants during photosynthesis process. But 6C14is a β-emitter and decays back into nitrogen as

$$_6C^{14} \rightarrow _7N^{14} + _{-1} e^0$$

As the living planet performs photosynthesis, the decay of C14 is compensated by a new supply of it from atmosphere air and a radioactive equilibrium is reached where there is a fixed ratio of 6C14 to 6C12.

Suppose the activity of some dead material was R0 at the time of death and it has been reduced to R after t years. Then, according to law of radioactive decay, we have

\begin{align*} R &= R_0 e^{-\lambda t} \\ \text {or,} e^{-\lambda t} &= \frac {R_0} {R} \\ \text {Taking log on both sides } \\ \text {or,} \lambda t &= \log _e \left (\frac {R_0}{R} \right ) \\ \text {or,} t &= \frac {1}{\lambda } \log _e \left (\frac {R_0}{R} \right ) \\ \therefore t &= \frac {1}{\lambda } \log _e \left (\frac {R_0}{R} \right ) \\ \text {But} \: \lambda = \frac {0.693}{T} ,\ \end{align*} where T = 5730 years, the half of the radioactive carbon. So\begin{align*} \\ t &= \frac {T}{0.693 } \log _e \left (\frac {R_0}{R} \right ) \\ \end{align*}

Hence by measuring the activity R0 of living plant and activity R of its dead material, the age t of that object can be determined.

#### Health Hazards and Safety Precautions

Following types of damages can be caused by the radiation hazards:

1. The exposure to radiation induces deleterious genetic effects.
2. The strong α-ray exposure can cause lung cancer.
3. The exposure to fast and slow neutron can cause blindness.
4. The exposure to neutrons, protons and α-particle can cause damage to red blood cells.
5. The strong exposures to protons and neutrons can cause serious damage to reproductive organs.

Following are safety precautions for radiation hazards

1. The radioisotopes should be transferred in thick walled lead containers and kept in rooms with thick walls of lead.
2. The radioisotopes are handled with the help of remote control device.
4. The radioactive contamination of the working area is avoided at all costs.
5. Nuclear explosions should be carried out far away from the public area.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.