Radioactivity

The spontaneous transformation of an element into another with the emission of some particle (or particles) or electromagnetic radiation is called natural radioactivity.

Laws of Radioactivity Decay

Rutherford and Soddy studied the phenomenon of radioactivity in details and formulated the following laws, known as the laws of radioactive decay:

1. Radioactivity is a spontaneous phenomenon and one cannot predict, when a particular atom in a given radioactive sample will undergo disintegration.

2. When a radioactive atom disintegrates, either an D-particle (nucleus of helium) or a E-particle (electron) is emitted.

3. The emission of an -particle by a radioactive atom results in a daughter atom, whose atomic number is 2 units less and mass number is 4 units less than that of the parent atom.

4. The emission of a β-particle by a radioactive atom results ina daughter atom, whose atomic number is 1 unit more but mass number is same as that of the parent atom.

5. The number of atoms disintegrating per second of a radioactive sample at any time is directly proportional to the number of atoms present at that time. The rate of disintegration of the sample cannot be altered by changing the external factors, such as pressure, temperature etc. It is known as radioactive decay law.

According to radioactive decay law, the rate of disintegration at any time t is directly proportional to the number of atoms present at time t i.e.,

or .

Where the constant of proportionally O is called decay constant of the radioactive sample. It is also known as disintegration constant or transformation constant. Its value depends upon the nature of the radioactive sample. Further, the negative sign indicates that the number of the atoms of the sample decreases with the passage of time.

From equation, we have

or

or

Radioactive Decay Constant

According to radioactive decay law, integrating, we have

or,

Hence, radioactive decay constant of a substance (radioactive) may be defined as the ratio of its instantaneous rate of disintegration to the number of atoms present at that time.

Again,

If

Then,

Hence, radioactive decay constant of a substance may also be defined as the reciprocal of the time, after which the number of atoms of a radioactive substance decreases to 0.368 (or 36.8%) of their number present initially.

Half Life

Consider that a radioactive sample contains atoms at time t = 0. Then, the number of atoms left behind after time t is given by

From the definition of half-life, it follows that when,

Setting the above condition in equation, we have

or,

or,

or,

Thus, half-life of a radioactive substance is inversely proportional to its decay constant and is characteristic property of its nucleus. It cannot be altered by any known method.

Mean Life or Average Life

The Average life of a radioactive substance is defined as the average time for which the nuclei of the atoms of the radioactive substance exist. It is defined by

Activity of radioactive substance

The activity of a radioactive substance may be defined as the rate at which the nuclei of its atoms in the sample disintegrate.

If a radioactive sample contains N atoms at any time t, then its activity at time t is defined as

The negative sign shows that with the passage of time, the activity of the radioactive substance decreases.

Since according to the radioactive decay law,

The equation may be expressed as, . Since, we have

Here, is activity of the radioactive sample at time t = 0.

Units of Activity

The activity of a radioactive sample may be expressed as disintegration per second. The practical unit of activity of a radioactive sample is curie (ci).

The activity of a radioactive sample is called one curie, if it undergoes disintegrations per second. Thus,

1 curie (ci) = disintegrations

There is also another unit of radioactivity, called Rutherford (rd).

The activity of a radioactive sample is called one Rutherford, if it undergoes disintegration per second.

1 Rutherford (rd) disintegration.