Problem 7 - Chemistry Matter and Change

Question

Thorium-229 is used to increase the lifetime of fluorescent bulbs. What type of decay occurs when thorium-229 decays to form radium-225?

Step-by-Step Solution

Answer

Thorium-229 decays to form Radium-225 through alpha decay, where an alpha particle containing 2 protons and 2 neutrons is emitted, resulting in a decrease of the atomic number by 2 and the mass number by 4.

Step 1: Identify the Given Information

We are given the initial isotope, Thorium-229, and the final product, Radium-225. To determine the decay type, we will look at the difference in atomic numbers and mass numbers between these two isotopes.

Step 2: Write Down the Atomic Numbers and Mass Numbers

The atomic number (Z) is the number of protons in the nucleus of an atom. The mass number (A) is the total number of protons and neutrons in the nucleus. For Thorium-229 (Th-229) and Radium-225 (Ra-225), we have the following information: Thorium-229: \(Z_{Th} = 90\), \(A_{Th} = 229\) Radium-225: \(Z_{Ra} = 88\), \(A_{Ra} = 225\)

Step 3: Identify the Change in Atomic Numbers and Mass Numbers

By comparing the atomic numbers and mass numbers of the two isotopes, we can determine the change in these values during the decay process: Change in atomic number: \(\Delta Z = Z_{Ra} - Z_{Th} = 88 - 90 = -2\) Change in mass number: \(\Delta A = A_{Ra} - A_{Th} = 225 - 229 = -4\)

Step 4: Determine the Type of Decay

When the change in atomic number is -2 and the change in mass number is -4, this indicates that the decay type is alpha decay. In alpha decay, an atom emits an alpha particle, which is composed of 2 protons and 2 neutrons (total mass number of 4). This results in the parent nucleus losing 2 protons, and hence, the atomic number decreases by 2. So, the type of decay that occurs when Thorium-229 decays to form Radium-225 is alpha decay.

Key Concepts

Radioactive Decay

Radioactive decay is a fundamental concept in physics and chemistry that describes the process by which an unstable atomic nucleus loses energy by emitting radiation. This spontaneous transformation can result in the production of different elements and isotopes.

For example, a heavy nucleus such as that of Thorium-229 tends to achieve stability through the emission of an alpha particle, leading to the formation of a new element, as seen when it decays to Radium-225. Radioactive decay is unpredictable for individual atoms, but it is statistically predictable for a large number of atoms, which is why we can use the half-life to describe its rate for a collection of atoms.

The three main types of radioactive decay are alpha, beta, and gamma decay, with alpha decay being the focus here. Each type of decay involves the release of different particles; alpha decay specifically releases an alpha particle, which consists of two protons and two neutrons, thus impacting both the atomic number and the mass number of the original element.

Nuclear Chemistry

Nuclear chemistry is the branch of chemistry that deals with changes in the nucleus of atoms. This field encompasses a variety of processes, including radioactive decay, nuclear fission, and nuclear fusion. These transformations are quite distinct from chemical reactions, which involve only the electrons of an atom and do not affect the atomic nucleus.

In the context of nuclear decay, nuclear chemistry focuses on how an unstable nucleus can regain stability. Alpha decay, as the solution to our exercise indicates, is one way this can be achieved. This involves the emission of an alpha particle, significantly altering the identity of the original atom and leading to the creation of a new element with different chemical properties.

Isotopes

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This means they have the same atomic number but different mass numbers.

Thorium-229 and Radium-225 are both examples of isotopes; one of Thorium and the other of Radium. Although isotopes of an element share chemical properties due to the same number of electrons, they often have different nuclear stability. The process of alpha decay seen in Thorium-229 changing to Radium-225 demonstrates how one isotope can transform into a different element altogether, creating a new isotope with distinct nuclear characteristics. Understanding isotopes is crucial in fields like nuclear medicine, radiometric dating, and nuclear power generation, highlighting their significant impact on science and technology.