Half-life Study Guide

1.3 Half-life (Chem.1.3)

Explore this Phenomenon

The graph above shows the half-life of carbon-14.

1. What is happening to the amount of carbon-14 isotope over time?
2. What does the exponential curve in the graph represent?

 

Standard Chem.1.3

Use mathematics and computational thinking to relate the rates of change in quantities of radioactive isotopes through radioactive decay (alpha, beta, and positron) to ages of materials or persistence in the environment. Emphasize a conceptual understanding of half-life. Examples could include radiocarbon dating, nuclear waste management, or nuclear medicine. (PS1.C)

While reading this section discover why and how the nucleus of an atom changes . What is the rate at which it changes?

 

Types of Radioactive Decay

In ordinary chemical reactions and processes, atoms of one element never change into different elements. The protons in the nucleus of an atom determines the identity of that element. Most chemical changes are related to changes with the electrons of atoms. In these nuclear decay processes the nucleus, which contains protons and neutrons, is changing. All nuclei with 84 or more protons are radioactive and elements with less than 84 protons have both stable and unstable isotopes. All these elements can go through nuclear changes and turn into different elements.

Isotopes of elements that have an unstable ratio of protons to neutrons in the nucleus of atoms tend to break down and release energy in the form of radiation like alpha, beta, and positron emissions. Oxygen isotopes all have 8 protons but Oxygen-16 has 8 neutrons while Oxygen-17 has 9 neutrons. Oxygen-17 will be unstable, and release radiation. Another example are the isotopes of Carbon, Carbon-12 and Carbon-14. Carbon-14 has more neutrons than Carbon-12 and is therefore, unstable.

 

Nuclear Decay Processes

Radioactive decay involves the emission of a particle and/or energy as one atom changes into another. In most instances, the atom changes its identity to become a new element . Discussed here are three types of emissions that occur.

 

Alpha Emission

Alpha (α) decay involves the release of helium ions from the nucleus of an atom . This ion consists of two protons and two neutrons and has a 2+ charge. Release of an α-particle produces a new atom that has an atomic number two less than the original atom and an atomic mass that is four less. A typical alpha decay reaction is the conversion of uranium-238 to thorium:

We see a decrease of two in the atomic number (uranium to thorium) and a decrease of four in the atomic mass (238 to 234). Usually the emission is not written with atomic number and mass indicated since it is a common particle whose properties should be memorized. Quite often the alpha emission is accompanied by gamma (γ) radiation, a form of energy release. Many of the largest elements in the periodic table are alpha-emitters. Emission of an alpha particle from the nucleus.

Beta Emission

Beta (β) decay is a more complicated process. Unlike the α-emission, which simply expels a particle, the β-emission involves the transformation of a neutron in the nucleus to a proton and an electron . The electron is then ejected from the nucleus. In the process, the atomic number increases by one while the atomic mass stays the same. As is the case with α-emissions, β-emissions are often accompanied by γ-radiation.

A typical beta decay process involves carbon-14, often used in radioactive dating techniques. The reaction forms nitrogen-14 and an electron:

Again, the beta emission is usually simply indicated by the Greek letter β; memorization of the process is necessary in order to follow nuclear calculations in which the Greek letter β without further notation.

 

Positron Emission

A positron is a positive electron (a form of antimatter). This rare type of emission occurs when a proton is converted to a neutron and a positron in the nucleus , with ejection of the positron. The atomic number will decrease by one while the atomic weight does not change. A positron is often designated by β + .

Carbon-11 emits a positron to become boron-11:

Gamma Emission

Gamma (γ) radiation is simply energy . It may be released by itself or more commonly in association with other radiation events. There is no change of atomic number or atomic mass in a simple γ-emission. Often, an isotope may produce γ-radiation as a result of a transition in a metastable isotope. This type of isotope may just “settle,” with a shifting of particles in the nucleus. The composition of the atom is not altered, but the nucleus could be considered more “comfortable” after the shift. This shift increases the stability of the isotope from the energetically unstable (or “metastable”) isotope to a more stable form of the nucleus.

 

Electron capture

Electron capture is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino. Following capture of an inner electron from the atom, an outer electron replaces the electron that was captured and one or more characteristic X-ray photons is emitted in this process. Following electron capture, the atomic number is reduced by one, the neutron number is increased by one, and there is no change in mass number.  Simple electron capture by itself results in a neutral atom, since the loss of the electron in the electron shell is balanced by a loss of positive nuclear charge. 

 

Penetrating Ability of Emissions

The various emissions will differ considerably in their ability to go through matter, known as their penetrating ability. The α-particle has the least penetrating power since it is the largest and slowest emission. It can be blocked by a sheet of paper or a human hand. Beta particles are more penetrating than alpha particles, but can be stopped by a thin sheet of aluminum. Of the three basic types of emissions, gamma particles are the most penetrating. A thick lead shield is required to stop gamma emissions. Positrons represent a special case in that they annihilate when they come in contact with electrons. The collision of a positron and an electron results in the formation of two gamma emissions that go 180 degrees away from each other.

Blocking of alpha particles can easily be accomplished by as little as 10 mm plastic or paper. Beta emissions represent a somewhat different situation. The negative charge on a beta particle has the potential for activating the element being used to block the radiation. Lead and tungsten are large atoms with many protons and neutrons in their nuclei. While the beta electron may be blocked, the target material could become irradiated in the process.

High-density materials are much more effective protection against gamma emissions than low-density ones. Gamma rays are usually blocked effectively by lead shielding. The thickness of the shielding will determine the effectiveness of the protection offered by the lead.

 

We’re putting it where?

Uranium isotopes produce plutonium-239 as a decay product. The plutonium can be used in nuclear weapons and is a power source for nuclear reactors , which generate electricity. This isotope has a half-life of 24,100 years, causing concern in regions where radioactive plutonium has accumulated and is stored. At some storage sites, the waste is slowly leaking into the groundwater and contaminating nearby rivers. The 24,100 year half-life means that it will be with us for a very long time.

 

Half-Life

Radioactive materials lose some of their activity each time a decay event occurs. This loss of activity can be estimated by determining the half-life of an isotope . The half-life is defined as that period of time needed for one-half of a given quantity of a substance to undergo a change. For a radioisotope, every time a decay event occurs, a count is detected on the Geiger counter or other measuring device. A specific isotope might have a total count of 30,000 cpm. In one hour, the count could be 15,000 cpm (half the original count). So the half-life of that isotope is one hour. Some isotopes have long half-lives – the half-life of U-234 is 245,000 years. Other isotopes have shorter half-lives. I-131, used in thyroid scans, has a half-life of 8.02 days.

This graph illustrates a typical decay curve for a radioactive material. The activity decreases by one-half during each succeeding half-life.

Typical radioactive decay curve.

 

Half-lives of different elements vary considerably, as shown in Table below:

Isotope	Decay Mode	Half-Life
Cobalt-60	Beta	5.3 years
Neptunium-237	Alpha	2.1 million years
Polonium-214	Alpha	0.00016 seconds
Radium-224	Alpha	3.7 days
Tritium (H-3)	Beta	12 years

 

We have talked about the activity and decay of individual isotopes. In the real world, there is a decay chain that takes place until a stable end-product is produced. For U-238, the chain is a long one, with a mix of isotopes having very different half-lives. The end of the chain resides in lead, a stable element that does not decay further.

 

Decay of uranium to stable end-product.

 

Putting It Together

Let us revisit this phenomenon:

1. How long is the half-life of carbon-14?
2. What percent of carbon-14 is left after 3 half-lives?