Problem 68 - Chemistry The Molecular Nature of Matter

Question

Write the symbol of the nuclide that forms from cobalt- 58 when it decays by electron capture.

Step-by-Step Solution

Answer

The nuclide that forms from cobalt-58 after electron capture is \(_{26}^{58}Fe\).

Step 1: Understand Electron Capture

Electron capture is a type of beta decay where an electron from the innermost energy level is captured by the nucleus, combining with a proton to form a neutron. The atomic number decreases by 1 because the atom loses a proton, but the atomic mass number remains unchanged because a neutron is formed.

Step 2: Identify the Original Nuclide

Cobalt-58 is represented by the symbol \(_{27}^{58}Co\) where 27 is the atomic number (number of protons) and 58 is the atomic mass number (number of protons plus neutrons).

Step 3: Determine the New Nuclide After Electron Capture

After the electron capture by cobalt-58, the atomic number decreases by 1, becoming 26 (which is the atomic number of iron, Fe), while the atomic mass number remains 58. Therefore, the new nuclide symbol is \(_{26}^{58}Fe\).

Key Concepts

Beta Decay

Beta decay is a form of radioactive decay where an unstable atomic nucleus transforms and emits a beta particle. This particle may be an electron (in beta-minus decay) or a positron (in beta-plus decay). During beta-minus decay, a neutron in the nucleus is converted to a proton, an electron, and an electron antineutrino. Conversely, beta-plus decay involves the transformation of a proton into a neutron, a positron, and an electron neutrino.

Electron capture, a subset of beta decay, is the process where an inner orbital electron is captured by the nucleus, leading to the conversion of a proton into a neutron and the emission of an electron neutrino. This process decreases the atomic number by one while leaving the atomic mass number unchanged, which is crucial in understanding the changes undergone by the nucleus during this type of decay.

Nuclide Symbols

Nuclide symbols are a concise way of representing the identity and composition of an atom's nucleus. The symbol for a nuclide is written as \( _{Z}^{A}\text{X} \) where \(\text{X}\) is the chemical symbol of the element, \(Z\) represents the atomic number indicating the number of protons, and \(A\) stands for the atomic mass number, the sum of protons and neutrons in the nucleus.

For example, the nuclide symbol for cobalt-58 is \( _{27}^{58}\text{Co} \) which denotes an isotope of cobalt having 27 protons and a total of 58 nucleons (both protons and neutrons combined). Nuclide symbols are crucial for understanding nuclear reactions, such as beta decay, where changes in the atomic number and nucleon count are represented by different symbols before and after the event.

Atomic Mass Number

The atomic mass number, denoted as \(A\), is a fundamental characteristic of a nuclide that determines its mass and stability. It is the sum of the number of protons \( (Z) \) and neutrons \( (N) \) in an atom's nucleus, thus \(A = Z + N\). This number is always an integer and is crucial in determining the isotope of an element.

For example, in the nuclide \( _{27}^{58}\text{Co} \), 58 is the atomic mass number, indicating that the cobalt nucleus contains a combined total of 58 protons and neutrons. When discussing nuclear reactions such as electron capture, it's important to note that the atomic mass number remains the same before and after the reaction since only the type of nucleon (proton to neutron) changes, not the total number of nucleons.