Half-life

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DEFINITION AND PROPERTIES

DEFINITION:

Radioactivity as its name might sound so complex is simply the process by which unstable atoms are converted to stable atoms with the emission of particles and electromagnetic radiation. Most atoms are unstable because they have a heavy nuclei so liberate EM radiations and particles in order to achieve stability.

Radioactivity is therefore the random and spontaneous emission of particles and EM radiations from the nucleus of an unstable atom. This process is termed random because it occurs on its own and spontaneous because it has no set pattern. However there exists basically 2 types of radioactivity; Natural and Artificial (induced or man-made) radioactivity.

In natural radioactivity, the nucleus disintegrates on its own whereas in artificial radioactivity the nucleus is activated with a highly energetic particle to bring about decay.

PROPERTIES:

The 3 main particles emitted during a radioactive decay are alpha(α), beta(β) and gamma  radiations.

 Figure 6

1 Alpha particles

Alpha rays or alpha particles are the positively charged particles. A highly energetic helium nucleus which contains two protons and two neutrons is called an alpha-particle.

 Figure 7: Alpha particle

Alpha particles have the least penetration power but the greatest ionization power. They cannot penetrate the skin but this does not mean that they are not dangerous. Since they have a great ionization power, so if they get into the body they can cause serious damage. They have the ability of ionizing numerous atoms  at a short distance. It is due to this reason that the radioactive substance that releases alpha particles needs to be handled with rubber gloves. It should not be inhaled, eaten or allowed near open cuts.

2 Beta particles

Beta particles are highly energetic electrons which are released from inside of a nucleus. They are negatively charged and have a negligible mass.

Figure 8: Beta Particle Emission

On the emission of a beta particle, a neutron in the nucleus divides into a proton and an electron. The beta particle is thus the electron that is rejected from the nucleus at high speed. Beta particles have a greater penetration power than the alpha particles and can easily travel through the skin. Though beta particles have less ionization power than the alpha particles but still they are dangerous and so their contact with the body must be avoided.

The waves from the high frequency end of the electromagnetic spectrum which do not have any mass are called the gamma rays. They have greatest power of penetration.

They are the least ionizing but most penetrating and it is extremely difficult to stop them from entering the body. These rays carry huge amount of energy and can even travel through thin lead and thick concrete.

Most of the properties of alpha, beta and gamma particles have been already discussed.

The table below gives a summary on the characteristics of alpha, beta and gamma radiations.

 Property α ray β ray ray Nature Positive charged particles, 2He4nucleus Negatively charged particles (electrons). Uncharged γ~0.01a,  electromagnetic radiation Charge +2e –e 0 Mass 6.6466 × 10–27 kg 9.109 × 10–31 kg 0 Range ~10 cm in air, can be stopped by 1mm of A l Upto a few m in can be stopped~cm of A l Several m in air stopped by~cm of Pb Natural Sources By natural radioisotopes e.g.92U236 By radioisotopes e.g.29Co68 Excited nuclei formed as a result of α, β decay

Radioactive decay also called nuclear decay is the process whereby an unstable atomic nucleus loses energy by emitting radiation which could be alpha, beta or gamma rays so as to become stable.

Therefore there exists 3 types of radioactive decay which are; α,β and gamma  decay.

v  ALPHA DECAY: When a parent nucleus undergoes an alpha decay, the mass number of the daughter nuclei becomes 4 less than that of the parent nucleus and the atomic number of the daughter nuclei becomes 2 less than that of the parent nucleus.

$^A_BX$ $^A_B^-_-^4_2Y$ + $^4_2He$

BETA DECAY: When a parent nucleus undergoes a beta decay, the mass number of the daughter nuclei remains unchanged while the atomic number of the daughter nuclei becomes 1 greater than that of the parent nucleus.

$^A_BX$$^A_B_+_1Y$+  $_-_1^0e$

v     GAMMA DECAYGamma decay mostly occurs when a nuclei which has undergone maybe and alpha or beta decay still remains unstable. The excess energy within this nuclei is emitted as gamma radiation for the nuclei to attain full stability. Therefore when a parent nucleus undergoes gamma decay, the mass number and atomic number of the daughter nuclei remains unchanged.

$^A_BX$$^A_BY$ + γ

HALF-LIFE

The half-life of a radioactive isotope is the time taken for the activity of the radioactive isotope to fall to half its original value. Iodine-131 has a half-life of 8.1 days, this means that half of it (iodine-131) will remain after 8.1 days.

Since radioactive decay is as a result of changes in the nucleus, external factors like temperature, pressure and pH will not affect the radioactivity of a radioactive decay hence will not affect the half-life as well.

 Figure 9: Half life sketch

Figure 10

Half life denoted as $t_\frac{1}{2}$ can be calculated using the formular below.

$t_\frac{1}{2}=\frac{In2}{\lambda&space;}$

where $t_\frac{1}{2}$= half life of radioactive isotope

$\lambda$=Decay constant

DECAY CONSTANT

The decay constant is the ratio of the number of atoms of a radionuclide that decay in a given period of time compared with the total number of atoms of the same kind present at the beginning of that period. The unit is per time ( $hr^-^1,s^-^1$).

 Figure 12: Decay Constant

The decay constant is gotten from the half-life using the formula below.

$\lambda&space;=\frac{In2}{t_\frac{1}{2}}$

Radioactivity has many medical, industrial and agricultural uses, some of which include;

1.   Some radiations are used to sterilize medical equipment and food.
2.   Radiation is used and produced in nuclear reactors which controls fission reactions to produce energy.
3.   In medicine, cobalt-60 is extensively employed as a radiation source to arrest the development of cancer.
4.   X rays are used in radiology to see whether bones are broken.
5.   Radioactive exposures improves the quality and productivity of some agricultural products along with insect and pest disease management.
6.   Some radioactive isotopes are used to detect flaws and
7.   Leakages on some industrial apparatus.

BINDING ENERGY

The binding energy is the energy required to separate an atomic nucleus completely in to its constituent protons and neutrons in order words, it is the energy that would be liberated by combining individual protons and neutrons in to a single nucleus. This energy is equal to the mass defect (Δm) which corresponds to the difference between the mass of the nucleus and that of the individual protons and neutrons.

Figure 14 : Binding Energy

This energy is calculated using Einstein’s equation of mass defect which states.

$E=\Delta&space;mc^2$

Where E= Binding energy.

C=speed of light in free space

$c=2.997\times&space;10^8m/s$

HOW BINDING ENERGY AFFECTS NUCLEAR STABILITY:

Nuclei with very low or very high mass numbers have lesser binding energy per nucleon hence are less stable because the lesser the binding energy per nucleon, the easier it nucleus in to its constituent nucleons (protons and neutrons).