Problem 75 - General Chemistry: Principles and Modern Applications

Question

5\. In your own words, define the following symbols: (a) \(\alpha ;\) (b) \(\beta^{-} ;\) (c) \(\beta^{+} ;\) (d) \(\gamma ;\) (e) \(t_{1 / 2}\).

Step-by-Step Solution

Answer

The given symbols are: \(\alpha\) representing alpha particles (helium nucleus) emitted during alpha decay, \(\beta^{-}\) representing electron emitted during beta minus decay, \(\beta^{+}\) representing positron emitted during beta plus decay, \(\gamma\) representing gamma rays in gamma emission, and \(t_{1/2}\) representing half-life of a radioactive substance.

Step 1: Define Alpha

\(\alpha\) stands for alpha particles. These are high energy particles that are emitted by certain types of radioactive substances during what is known as alpha decay. An alpha particle is composed of two protons and two neutrons, essentially making it a helium nucleus.

Step 2: Define Beta negative

\(\beta^{-}\) stands for negative beta particles. Substance emits \(\beta^{-}\) particles during beta minus decay. A \(\beta^{-}\) particle is essentially an electron that is emitted from the nucleus of the atom when a neutron transforms into a proton.

Step 3: Define Beta positive

\(\beta^{+}\) stands for positive beta particles. Certain substances emit \(\beta^{+}\) particles during beta plus decay. A \(\beta^{+}\) particle is essentially a positron, that is emitted from the nucleus of the atom when a proton transforms into a neutron.

Step 4: Define Gamma

\(\gamma\) stands for gamma rays. Gamma rays are high energy photons emitted by a radioactive atom. This symbol is often used to represent a type of nuclear decay known as gamma decay, where a nucleus in an excited state emits a gamma ray to reach a lower energy state.

Step 5: Define Time Half-life

\(t_{1/2}\) stands for the half-life of a radioactive substance. It is the time required for half of the atoms in a sample of a particular radioactive substance to decay or transform. This process continues until all the unstable atoms have decayed.

Key Concepts

Alpha Decay

Alpha decay is a form of radioactive decay where an unstable atomic nucleus emits an alpha particle, which consists of two protons and two neutrons. This release transforms the original atom into a new element with an atomic number that is two less and a mass number four less than the original atom. For example, when Uranium-238 undergoes alpha decay, it becomes Thorium-234.

As alpha particles are relatively heavy and carry a double positive charge, they have a short range and can be stopped by a sheet of paper or the outer layer of human skin. Despite their lack of penetrating power, alpha particles can cause significant damage to living tissue if ingested or inhaled. Understanding alpha decay is critical in fields such as nuclear physics, radiometric dating, and nuclear medicine.

Beta Decay

Beta decay represents a category of radioactive decay wherein an unstable atom experiences a transformation within its nucleus, resulting in the emission of beta particles. There are two forms of beta decay: beta-minus (β-) and beta-plus (β+).

During beta-minus decay, a neutron in the nucleus converts into a proton, emitting an electron (the beta particle) and an anti-neutrino. Conversely, beta-plus decay involves a proton changing into a neutron with the release of a positron (the positive beta particle) and a neutrino. This process is significant because it helps transmutate an atom into another element and is essential in applications like medical imaging with positron emission tomography. While beta particles have greater penetrating power than alpha particles, they are still relatively easy to shield against, with materials like plastic or glass often being sufficient.

Gamma Rays

Gamma rays, denoted by the Greek letter γ, are the highest energy form of electromagnetic radiation and are emitted by the nucleus of a radioactive atom during gamma decay. This process occurs when the nucleus remains in an excited state following other types of decay, such as alpha or beta decay, and releases this excess energy in the form of a gamma photon.

Gamma rays have no mass or charge, which allows them to penetrate matter much more effectively than alpha or beta radiation. Due to their high energy, they can travel significant distances through air and require dense materials, like lead or thick concrete, for effective shielding. Gamma rays are applied in various sectors, including medical treatments like cancer radiotherapy, industrial imaging, and as a diagnostic tool in nuclear medicine.

Half-life

Half-life, symbolized as t_1/2, is a fundamental concept in the study of radioactive decay. It is the amount of time required for half the atoms in a given sample of a radioactive isotope to decay into other elements or isotopes. Each radioactive element has a unique half-life, which can range from fractions of a second to billions of years.

The concept of half-life is crucially important for understanding the long-term behavior of radioactive substances, whether they are used in medical diagnostics, determining the ages of archaeological artifacts through carbon dating, or managing the decay of nuclear waste. Since the decay process is random but statistically predictable, half-lives help scientists and engineers calculate the necessary safety measures and timings for the use of radioactive materials.