Wednesday, February 4, 2015

Radio Activity and Half Life Period

Spontaneous emission of Alpha, beta and gamma radiation from the unstable nuclei is called radioactivity. This generally happens with the heavy nucleus like uranium and thorium. We cannot change the radioactivity by playing high-temperature, high-pressure or electric field. Nuclei can disintegrate immediately or it may take in finite time.

Alpha decay

The Alpha particle is nothing but a helium nucleus. It is a positively charged particle whose charge is equal to two times a charge of the photon. It is deflected both electric and magnetic fields.

With the emission of the Alpha particle, the atomic number of the nucleus is reduced by two and its mass number is reduced by four.

Beta decay

The emission of the fast moving electrons from the nucleus is called beta decay. The neutron inside the nucleus splits up into proton and electron. The electron is rejected out like beta particle. The proton reminds inside the nucleus itself. Because of this the atomic number is increased by one when there is emission of beta particle will. Anyway the mass number of the nuclei is going to remain same as the number of the neutrons decreases by one and the number of the protons increases by one.

As the beta particles are having a charge they are also deflected by electric and magnetic fields. They have ionization power less than that of Alpha particles and penetration power better than that of Alpha particles.

Gamma Decay

Gamma rays are nothing but electromagnetic radiation of short wavelength. There is no effect on atomic number as well as the mass number during this emission. During the emission of Alpha Ray and beta Ray electrons goes to excited states. They cannot stay in the excited state for a long time and they will come back to their earlier states. 

During this process they emit some energy and that energy is observed in the form of this electromagnetic waves. Gamma rays alone cannot be emitted. As a consequence of Alpha Ray or beta Ray, they can be emitted.

Law of radioactivity

Basing on experimental observations and analysis of radioactive material this is formulated. According to this law the rate of radioactive decay at any instant is directly proportional to number of nuclei present at that instant and is independent of physical conditions like temperature, pressure and chemical composition. Radioactive decay is nothing but the number of the nuclei decaying per unit time.

We can derive the relation between number of the nucleons present with respect to the initial number of the nucleons after a specified time as shown below.

Half life period

The time interval during which the number of radioactive nuclei of a sample disintegrates to half of its original number of nuclei is called a half life period.

We can derive the relation between half life period and the decay constant basing on their respective definitions as shown below.

Half life period of a material is its characteristic property and it cannot be changed by any of the known methods. We can express the relation between the initial number of nucleons and the final number of nucleons with respect to number of the half lives as shown below.

It can be mathematically noticed that after half of the half life period 70.7% of the initial number of the nucleons are going to be present. It means approximately 30% of the nucleons were disintegrated in the first half of the half life period. You might notice that it is not 25% but 30% . More disintegration is happened because initially there are more number of nucleons.

Average life

The phenomenon of radioactivity is random and we cannot predict which one of the atoms will decay first and when. Each atom will decay in its one-time and to determine the average of all the decays, we have defined average life. It is defined as the ratio of total lifetime of all the nucleons to the number of nuclei. It can be mathematically proved as the reciprocal of the decay constant. We can derive the relation between half life period and the average life as shown below.

Problem and solution

The half-life period of the Cobalt is 72 years. How much time does it take for three by fourth of its initial mass to disintegrate?

We can solve this problem basing on the Basic derivation is that we have made in the above pages. We can calculate the number of half life period is as shown below.

Problem and solution

A radioactive sample can decay in two different processes simultaneously with a different half life periods. Find the effective half liquidate of the sample?

We can solve this problem basing on the law radioactive decay. According to this law the number of the nucleons disintegrated per second is directly proportional to initial number of nucleons. The same element is going through two different processes and hence the initial number of the nucleons are same. The total rate of disintegration is equal to the sum of rate of disintegration of both the cases. We can solve this problem as shown below.

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