Question

\(^{39} \mathrm{Ar}\) is an isotope with a half-life of \(269 \mathrm{yr}\). If it decays through beta-minus emission, what isotope will result?

Short answer

Answer: The resulting isotope after beta-minus decay of \(^{39} \mathrm{Ar}\) is \(^{39} \mathrm{K}\).

Step-by-step solution

Understand Beta-Minus Decay

In beta-minus decay, a neutron in the nucleus is converted into a proton. This process results in an electron (called a beta particle) and an electron antineutrino being emitted from the nucleus. The atomic number increases by 1 during this process and the mass number remains unchanged since a proton is taking the neutron's place.

Identify the Isotope

The given isotope is \(^{39} \mathrm{Ar}\), which means it has an atomic number of 18 (since Argon is element number 18) and a mass number of 39.

Determine the New Atomic Number and Mass Number

Since beta-minus decay increases the atomic number by 1, the new atomic number will be 18 + 1 = 19. The mass number will remain unchanged, so it stays at 39.

Identify the Resulting Isotope

With an atomic number of 19, the resulting element is potassium (K). Therefore, the resulting isotope is \(^{39} \mathrm{K}\) after beta-minus decay.

Key concepts

Radioactive Decay

Radioactive decay is a natural process by which an unstable atomic nucleus loses energy by emitting radiation. During this process, the nucleus of an atom will release particles until it becomes more stable. There are several types of radioactive decay, including alpha decay, beta decay (which includes beta-minus and beta-plus), and gamma decay. Each type results from a different interaction within the atom's nucleus and results in different products and radiation types.

For example, in beta-minus decay, a common type of radioactive decay, a neutron is transformed into a proton, an electron (known as a beta particle), and an antineutrino; the emitted beta particle is what gives this decay its name. This transformation changes the identity of the parent atom because the number of protons in the nucleus, which determines the element's identity, increases by one. Thus, a new element emerges following beta-minus decay.

Isotopes

Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. Essentially, isotopes of an element have the same number of protons in the nucleus (which defines what element it is) but a different number of neutrons. This difference in neutron number can make some isotopes unstable, leading them to undergo radioactive decay to achieve stability.

An example is Argon-39 (\( ^{39}\text{Ar} \)), which contains the same number of protons as every other argon atom (18 protons), but it has a unique number of neutrons that makes it unstable. Such unstable isotopes are also known as radioisotopes, and their decay processes can be valuable both in scientific research and in practical applications such as medical imaging and radioactive dating.

Nuclear Physics

Nuclear physics is the branch of physics that studies the constituents and interactions of atomic nuclei. Fundamental to understanding radioactive decay, nuclear physics explores the behavior of nuclear particles like protons and neutrons. This field explains how energy is generated in nuclear reactions, an understanding vital for nuclear power and nuclear weapons. It also is essential for explaining how stars generate energy and how elements are formed within them through nuclear fusion and other processes.

Through nuclear physics, we can comprehend phenomena such as beta-minus decay and harness the energy released from nuclear reactions efficiently and safely. This branch of physics also underpins the techniques used to determine the properties of isotopes and predict their stability and potential decay pathways.

Half-life

The half-life of a radioactive isotope is the time required for half of the atoms in a sample to undergo decay. This concept is crucial for understanding the rate at which radioactive materials transform over time. Half-life is a measure of the stability of a radioisotope; the longer the half-life, the more stable the isotope. Each radioactive isotope has a characteristic half-life that is not affected by external conditions such as temperature or pressure.

Argon-39, for instance, has a half-life of 269 years, meaning that after 269 years, half of a given sample of Argon-39 will have decayed into another element, in this case, potassium-39 (\( ^{39}\text{K} \)). Half-life information is employed in various fields, including geology for dating rocks and archaeology for dating artifacts, as well as in medicine for assessing exposure times for radioactive treatments.