Question

When a nuclide produces a beta particle, the atomic number of the resulting new nuclide is one unit than that of the original nuclide.

Short answer

In conclusion, when a nuclide undergoes β- decay and emits a beta particle, the atomic number of the resulting new nuclide increases by one unit. The general equation for β- decay is: \(X(A, Z) \rightarrow X'(A, Z+1) + e^- + \bar{\nu}_e\) where X is the original nuclide and X' is the new nuclide formed after β- decay. New Atomic Number (Z') = Original Atomic Number (Z) + 1.

Step-by-step solution

Understand Beta Decay

Beta decay is a process in which unstable nuclides transmute into a more stable nuclide by emission of a beta particle. There are two types of beta decay: beta minus (β-) and beta plus (β+) decay. In this exercise, we'll focus on β- decay since that is what the exercise mentions.

Beta Minus Decay

In β- decay, a neutron within an unstable nucleus is converted into a proton while emitting an electron (called a beta particle) and an electron antineutrino. During this process, the atomic number of the nuclide increases by one unit while the mass number remains the same. The general equation for β- decay is: \(X(A, Z) \rightarrow X'(A, Z+1) + e^- + \bar{\nu}_e\) where: - X is the original nuclide with atomic number Z and mass number A - X' is the new nuclide formed after β- decay - \(e^-\) is the emitted beta particle (electron) - \(\bar{\nu}_e\) is the emitted electron antineutrino

Determine the New Atomic Number

From the β- decay equation, we can determine the atomic number of the new nuclide (X') by simply adding one unit to the atomic number of the original nuclide (X). New Atomic Number (Z') = Original Atomic Number (Z) + 1 In conclusion, when a nuclide undergoes β- decay and emits a beta particle, the atomic number of the resulting new nuclide increases by one unit.

Key concepts

What is a Nuclide?

A nuclide is a technical term in nuclear chemistry and physics for a species of atom characterized by the constitution of its nucleus. The nucleus is defined by the number of protons it contains, known as the atomic number (Z), and the number of neutrons, referred to as the neutron number (N). Collectively, the sum of protons and neutrons is the mass number (A). Each nuclide is represented by a symbol on the periodic table and is uniquely identified by its atomic number and mass number, written as \( _Z^A\text{X} \). For instance, carbon-14, with 6 protons and 8 neutrons, is a different nuclide from carbon-12, which has 6 protons and 6 neutrons. While both are carbon atoms, their differing neutron numbers result in distinct properties, most notably, carbon-14 is radioactive, whereas carbon-12 is stable.

Understanding Atomic Number

The atomic number, denoted as Z, is a fundamental property of atomic nuclei that determines the identity of an element. It is the number of protons in the nucleus and, by charge neutrality, also equals the number of electrons in a neutral atom. The periodic table of elements is arranged in increasing atomic number, which results in the grouping of elements with similar chemical properties.When discussing nuclear processes like beta decay, the change in atomic number plays a crucial role because it transforms one element into another. This concept is integral to the nature of chemical reactions and the formation of new substances. A change in the atomic number means a change in the element's chemical identity, a phenomenon not seen in typical chemical reactions but rather in nuclear reactions.

What is Beta Minus Decay?

Beta minus decay (\(\beta^-\) decay) is a type of radioactive decay in which an unstable nucleus releases energy to become more stable. During this process, a neutron in the nucleus is transformed into a proton, and two particles are emitted: a beta particle (which is the same as an electron) and an electron antineutrino (\(\bar{u}_e\)).

As a result of this transformation, the atomic number of the nucleus increases by one, while the mass number stays constant. This is because a proton and a neutron have almost the same mass, but the identity of the element changes due to the increase in the number of protons. The emitted electron and antineutrino carry away the excess energy and momentum, allowing the nucleus to settle in a more stable configuration.

Electron Emission in Decay Processes

Electron emission, also known as beta particle emission, occurs in several types of decay processes, including \(\beta^-\) decay. When an electron is ejected from the nucleus during this decay, it is one of the main indicators that a nuclear transformation has occurred.

The emitted electron carries away excess energy from the decaying nuclide, which helps to lower its energy state towards stability. This emission is not something that occurs under normal circumstances with typical atomic electrons in their orbitals; it is a unique aspect of some nuclei's radioactive decay processes. The energy and speed at which these electrons are emitted can tell scientists a great deal about the decaying process and the nature of the forces within the nucleus.