Question

Thorium- 231 is the product of alpha emission. It is radioactive and emits beta radiation. Determine (a) the parent nucleus of Th-231. (b) the daughter product of Th-231 decay.

Short answer

Question: Identify the parent nucleus of Thorium-231 and the daughter product it forms after radioactive decay. Answer: The parent nucleus of Thorium-231 is Uranium-235, and the daughter product formed after radioactive decay is Protactinium-231.

Step-by-step solution

Understand alpha emission and beta radiation

In alpha emission, a nucleus emits an alpha particle which consists of 2 protons and 2 neutrons. Mathematically, we denote an alpha particle as ^4_2He, where 4 is the mass number (A), and 2 is the atomic number (Z). In beta radiation, a nucleus emits a beta particle, which is an electron. In this process, a neutron in the nucleus is converted into a proton. This increases the atomic number (Z) by 1 while keeping the mass number (A) constant.

Determine the parent nucleus of Th-231

Thorium-231 is formed as a result of alpha emission, so the parent nucleus must have lost an alpha particle. Using the notation mentioned earlier, we can represent the alpha emission as a simple equation: Parent nucleus -> ^{231}_{90}Th + ^4_2He We need to find the mass number (A) and the atomic number (Z) of the parent nucleus. Since the parent nucleus lost an alpha particle: A_parent = A_Th + A_alpha = 231 + 4 = 235 Z_parent = Z_Th + Z_alpha = 90 + 2 = 92 The parent nucleus has a mass number of 235 and an atomic number of 92. This corresponds to Uranium-235 (U-235). So, the parent nucleus of Th-231 is Uranium-235.

Determine the daughter product of Th-231 decay

Th-231 undergoes beta radiation decay, during which a neutron is converted into a proton. This process changes the atomic number by 1 while keeping the mass number constant: Daughter nucleus <- ^{231}_{90}Th + beta radiation To find the mass number (A) and the atomic number (Z) of the daughter nucleus, we use the following calculations, considering that the atomic number increases by 1: A_daughter = A_Th = 231 (mass number remains constant) Z_daughter = Z_Th + 1 = 90 + 1 = 91 The daughter nucleus has a mass number of 231 and an atomic number of 91. This corresponds to Protactinium-231 (Pa-231). So, the daughter product of Th-231 decay is Protactinium-231.

Key concepts

Alpha Emission

Alpha emission is a kind of radioactive decay where an unstable atomic nucleus releases an alpha particle, composed primarily of two protons and two neutrons. The symbol for an alpha particle is (^{4}_{2}He), which also denotes a helium nucleus. This emission leads to a reduction in the mass number of the original nucleus by four and a decrease in the atomic number by two, thus transforming the element into another.

For example, when Uranium-238 ((^{238}_{92}U)) undergoes alpha decay, it loses an alpha particle and becomes Thorium-234 ((^{234}_{90}Th)). During this process, both energy and the alpha particle are emitted, a characteristic that is harnessed in applications like smoke detectors and radiation therapy.

Understanding alpha emission is crucial as it helps explain the changes in an element's identity after decay. With elements like Uranium that undergo alpha decay, it explains how they eventually transmute into different elements after releasing energy and particles over time.

Beta Radiation

Beta radiation, by contrast, involves the emission of beta particles, which are high-energy, high-speed electrons or positrons. This form of decay occurs when a neutron in an unstable atomic nucleus is transformed into a proton and an electron is ejected from the nucleus. The ejected electron is referred to as a beta particle, and this process leads to an increase in the atomic number by one while keeping the mass number unchanged.

Let's look at it closer: if Thorium-231 ((^{231}_{90}Th)) undergoes beta decay, a neutron in its nucleus turns into a proton and an electron ((^{-}_{0}e)). This increases the atomic number from 90 to 91 without altering the mass number, forming Protactinium-231 ((^{231}_{91}Pa)).

Beta radiation is essential for medical treatments, such as in radiation therapy for cancer, and is also utilized in industrial applications where thickness testing of materials is required. Furthermore, an understanding of beta decay helps us in carbon dating, a method used to determine the age of archaeological findings.

Radioactive Decay

Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This process can take many forms, including alpha decay and beta radiation, as well as gamma decay and positron emission. The rate of decay is exponential and is characterized by each isotope's half-life, the time it takes for half of a sample of the isotope to decay.

The concept of radioactive decay is fundamental in nuclear physics and has a wide range of applications. For instance, it is the principle behind nuclear power generation and radiometric dating techniques. The decay process leads to the production of radiation that can potentially be harmful, so understanding it is critical for the safe handling and disposal of radioactive materials and for protecting the public from unnecessary exposure. Additionally, knowledge of radioactive decay processes enriches our understanding of the age and formation of natural elements within stars and the universe.