Question

Based on Figure \(1,\) if a nucleus of \(_{90}^{230} \mathrm{Th}\) underwent beta decay, which of the following nuclei would be produced? F. \(_{230}^{230} \mathrm{Pa}\) G. \(_{91}^{230} \mathrm{Pa}\) H. \(_{91}^{230} \mathrm{Th}\) J. \(_{231}^{91} \mathrm{Th}\)

Short answer

Answer: G. \(_{91}^{230} \mathrm{Pa}\)

Step-by-step solution

Identify the type of decay

Beta decay is a process in which a neutron in the nucleus is transformed into a proton or vice versa. There are two types of beta decay: beta-minus decay (β-) and beta-plus decay (β+). In β- decay, a neutron is converted to a proton, and in β+ decay, a proton is converted to a neutron.

Determine which beta decay occurs in this case

In this problem, we are not explicitly told whether the nucleus undergoes β- or β+ decay. However, since thorium is a heavy element, it is more likely to undergo β- decay, which results in an increase in the atomic number (number of protons).

Apply the beta-minus decay

In β- decay, a neutron is converted to a proton, increasing the atomic number by 1. Let's apply β- decay to the given nucleus: \(_{90}^{230} \mathrm{Th}\). Since the atomic number increases by 1, the new nucleus will have an atomic number of 91, and the mass number will remain 230.

Find the new element in the periodic table

Now, we need to find the element with an atomic number of 91. Referring to a periodic table, the element with an atomic number of 91 is protactinium (Pa).

Determine the correct option

In the problem, we're given four choices for the nucleus produced as a result of the beta decay of \(_{90}^{230} \mathrm{Th}\). Since the new element is protactinium (Pa) with an atomic number of 91 and the mass number remains 230, the correct option is: G. \(_{91}^{230} \mathrm{Pa}\)

Key concepts

Nuclear Chemistry

Nuclear chemistry delves into the intricate processes that take place within the cores of atoms—the nuclei. At its core, it involves studying reactions that alter the structure, composition, and energy of atomic nuclei. One of the most fundamental reactions in nuclear chemistry is beta decay, which encompasses the transformation of a neutron into a proton (beta-minus decay) or a proton into a neutron (beta-plus decay). Understanding beta decay not only clarifies how elements can change their identity but also underpins critical applications such as radiometric dating and medical diagnostics like PET scans.

Atomic Number

The atomic number is a fundamental characteristic of an element, representing the number of protons in the nucleus of an atom. It is denoted by the symbol Z. The atomic number fundamentally determines the chemical properties of an element because it defines the element's position in the periodic table. When a nucleus undergoes beta decay, the atomic number changes, essentially transforming the element into a new one. For instance, a beta-minus decay will increase the atomic number by 1, as a neutron converts to a proton, creating a different element with unique chemical properties.

Isotopes

An element can exist in different forms known as isotopes, which are variants of the element that have the same atomic number but different mass numbers (total number of protons and neutrons). Isotopes play a pivotal role in beta decay outcomes. Even though the element changes its identity after a beta decay, isotopes are uniquely identified by their mass number staying constant, hinting at their origin from the same element. This conservation of mass number despite the alteration in atomic identity is a cornerstone in understanding nuclear chemistry's influence on the composition of matter across the universe.

Periodic Table

The periodic table is a tabular display of all known chemical elements, ordained in increasing atomic number. It maps out the structure of atoms, including protons, neutrons, and electrons and provides a visual framework to understand how beta decay transforms one element into another. Materializing the connection between atomic number and elemental identity, the periodic table is a crucial tool in predicting the product of beta decay, as we use the atomic number to identify the new element formed. Students and chemists alike rely on the periodic table as a guide to comprehend the implications of nuclear transformations.