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Radioactive Decay: Definition, Formula & Types

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  • 0:00 Radioactive Decay and…
  • 1:55 A Review of Chemical Symbols
  • 2:33 Alpha Decay
  • 3:30 Beta Decay
  • 5:15 Gamma Emission
  • 6:00 Lesson Summary
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Lesson Transcript
Instructor: Nissa Garcia

Nissa has a masters degree in chemistry and has taught high school science and college level chemistry.

In this lesson, we'll discuss radioactive decay and learn the terms parent nucleus, daughter nucleus, and half-life. We'll also examine three types of radioactive decay.

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.

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.

In order to calculate the half-life of a radioactive material, we use the following equation:

Half-Life Formula

  • N0 is the initial quantity of the substance
  • N(t) is the quantity that still remains and has not yet decayed after a time (t)
  • t1/2 is the half-life of the decaying quantity
  • e is Euler's number, which equals 2.71828

For example, we can use the formula above to solve this 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?

Half-Life Example Problem

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

A Review of Chemical Symbols

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's 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. Let's talk about alpha decay first.

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, you'll 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 4 less than the original and an atomic number that is 2 less than the original. Since the atomic number is different, then the chemical element is also different

Here is the equation for the radioactive decay of uranium (U) to thorium (Th):

Alpha Decay Reaction

If we add all the superscripts from the product's 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 (a subatomic particle that is electrically neutral) or electron neutrino.

There are two types of beta decay, beta minus decay and beta plus 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.

Beta Minus Decay

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).

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