DECAY AND RADIOACTIVE HALF LIFE

Radioactive Decay and Half-Life

Radiation is part of our everyday lives. There are natural sources of radiation, such as radiation from outer space, as well as man-made sources of radiation, like nuclear power plants and cell phones.
Radiation is given off from a process called radioactive decay. Radioactive decay occurs when the original nucleus or parent nucleus of an unstable atom decomposes and forms a different nucleus or the daughter nucleus, as shown in the illustration below.

The rate at which radioactive decay occurs is measured using half-life, which is the time it takes for half the amount of the parent nucleus to decay. Each time the half-life of a radioactive material occurs, the amount of the radioactive material decreases to half of the original value, as shown in the illustration:
In order to calculate the half-life of a radioactive material, we use the following equation:
For example, we can use the formula above to solve the following problem:
The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 100 mg of Sr-90, how many milligrams will remain after 152.4 years?

Solution:
Here are the steps in calculation:
1. -0.693 multiplied by 152.4 = -105.6132
2. -105.6132 divided by 38.1 = -2.77
Here are the steps in calculation:
1. -0.693 multiplied by 152.4 = -105.6132
2. -105.6132 divided by 38.1 = -2.772
3. e raised to the power of -2.772 = 0.0625
4. 100 multiplied by 0.0625 = 6.25

Types of Radioactive Decay

When radioactive decay occurs, a particle or energy is emitted when the nucleus of the parent atom decays to the daughter nucleus. Before we proceed to the different types of decay, let us review that the atomic mass is the superscript or the small number at the upper left side of the element symbol, indicating how many protons and neutrons are in the nucleus, and the atomic number is the subscript or small number at the lower left side of the element symbol, indicating how many protons are in the nucleus.
There are three main types of radioactive decay. These are: alpha decay, beta decay and gamma emission.

Alpha Decay

Alpha decay or alpha emission is the release or emission of an alpha particle, which is a helium nucleus, consisting of two protons and two neutrons. This type of decay usually occurs in larger and heavier atoms. In the figure below, you will see that a helium particle (alpha particle) is emitted from the parent nucleus.
Due to the release of the alpha particle, the daughter nucleus has an atomic mass that is four less than the original and an atomic number that is two less than the original. Since the atomic number is different, then the chemical element is also different. See the radioactive decay of uranium (U) to thorium (Th) in the equation below:
If we add all the superscripts from the products side (234 + 4), it will be equal to the atomic mass of uranium, which is 238. If we add all the subscripts from the products side (90+2), it will be equal to the atomic number of the parent nucleus, uranium.

Beta Decay

Beta decay or beta emission occurs when a neutron transforms into a proton or a proton transforms into a neutron inside the nucleus. This conversion results in a beta particle - either an electron or positron - to be emitted, accompanied by either an electron antineutrino or electron neutrino. An electron neutrino is a subatomic particle that is electrically neutral, and an electron antineutrino is the antimatter counterpart of the electron neutrino. Beta decay typically looks like:
There are two types of beta decay, beta minus decay and beta plus decay.

• Beta Minus Decay

Beta minus decay occurs when a neutron turns into a proton. This causes an electron, accompanied by an electron antineutrino, to be emitted. As a result, the daughter nucleus' atomic number increases by 1.
Below are the symbols typically used for a beta minus decay. An example is shown where the iodine (I) undergoes radioactive decay, producing xenon (Xe). We can see that the atomic number increases. We can also see that an antineutrino is emitted.
If we check the superscripts (atomic masses) and subscripts (atomic numbers), they are balanced in the reactants and products: (131 = 131), and (53 = 54-1).

• Beta Plus Decay or Positron Emission