Question

Fill in the blanks in these radioactive decay series: (a) \(^{232} \mathrm{Th} \stackrel{\alpha}{\longrightarrow}\) _______ \(\stackrel{\beta}{\longrightarrow}\) ________ \(\stackrel{\beta}{\longrightarrow}{ }^{228} \mathrm{Th}\) (b) \({ }^{235} \mathrm{U} \stackrel{\alpha}{\longrightarrow}\) ________ \(\stackrel{\beta}{\longrightarrow}\) _________ \(\stackrel{\alpha}{\longrightarrow}^{227} \mathrm{Ac}\) (c) _______ \(\stackrel{\alpha}{\longrightarrow}{ }^{233} \mathrm{~Pa} \stackrel{\beta}{\longrightarrow}\) ___________ \(\stackrel{\alpha}{\longrightarrow}\) ________.

Short answer

The filled decay series are: (a) \(^{232} \mathrm{Th} \stackrel{\alpha}{\longrightarrow}{ }^{228} \mathrm{Ra}\)\(\stackrel{\beta}{\longrightarrow}{ }^{228} \mathrm{Fr}\) \(\stackrel{\beta}{\longrightarrow}{ }^{228} \mathrm{Th}\), (b) \({ }^{235} \mathrm{U} \stackrel{\alpha}{\longrightarrow}{ }^{231} \mathrm{Th}\) \(\stackrel{\beta}{\longrightarrow}{ }^{231} \mathrm{Pa}\) \(\stackrel{\alpha}{\longrightarrow}^{227} \mathrm{Ac}\), (c) \({ }^{237} \mathrm{Th} \stackrel{\alpha}{\longrightarrow}{ }^{233} \mathrm{~Pa} \stackrel{\beta}{\longrightarrow}{ }^{233} \mathrm{Th}\) \(\stackrel{\alpha}{\longrightarrow}{ }^{229} \mathrm{Fr}\)

Step-by-step solution

Solve for (a)

In alpha decay, atomic number decreases by 2 and atomic mass decreases by 4. Thus, after the alpha decay of Thorium 232, we get Radon 228.After the beta decay, the atomic number increases by one and we get Francium 228.After the second beta decay, we again increase the atomic number by one so we finally get Thorium 228. Hence, the series is: \(^{232} \mathrm{Th} \stackrel{\alpha}{\longrightarrow}{ }^{228} \mathrm{Ra}\)\(\stackrel{\beta}{\longrightarrow}{ }^{228} \mathrm{Fr}\) \(\stackrel{\beta}{\longrightarrow}{ }^{228} \mathrm{Th}\)

Solve for (b)

Using the same logic we infer that after alpha decay from Uranium 235, we get Thorium 231.After the beta decay, the atomic number increases by one so, we get Protactinium 231.After another alpha decay, we get Actinium 227. Hence, the series is: \({ }^{235} \mathrm{U} \stackrel{\alpha}{\longrightarrow}{ }^{231} \mathrm{Th}\) \(\stackrel{\beta}{\longrightarrow}{ }^{231} \mathrm{Pa}\) \(\stackrel{\alpha}{\longrightarrow}^{227} \mathrm{Ac}\)

Solve for (c)

The series starts with an alpha decay. So we increase the atomic number by 2 and the mass by 4 to the Pa-233, obtaining Thorium 237.The Thorium 237 then undergoes a beta decay, transforming into Protactinium 237. Lastly, after another alpha decay, the result is Francium 233. Hence, the series is: \({ }^{237} \mathrm{Th} \stackrel{\alpha}{\longrightarrow}{ }^{233} \mathrm{~Pa} \stackrel{\beta}{\longrightarrow}{ }^{233} \mathrm{Th}\) \(\stackrel{\alpha}{\longrightarrow}{ }^{229} \mathrm{Fr}\).

Key concepts

Alpha Decay

In the world of nuclear physics, alpha decay is a type of radioactive decay where an alpha particle is emitted from a heavy nucleus. An alpha particle is made up of 2 protons and 2 neutrons, essentially forming a helium nucleus. During alpha decay, the parent nucleus loses two protons and two neutrons, resulting in a decrease in atomic number by 2 and atomic mass by 4. This transforms the original atom into a new element entirely. For example, in the decay of thorium-232: - Thorium-232 undergoes alpha decay. - It transforms into radium-228. It's essential to understand this process because it explains how elements change over time naturally. Alpha decay often occurs among heavier elements like uranium and thorium because they are unstable and seek lower energy states by releasing alpha particles.

Beta Decay

Beta decay is another form of radioactive decay in which a beta particle—either an electron or a positron—is emitted from an atomic nucleus. This process changes a neutron to a proton or a proton to a neutron, leading to an increase or decrease in the atomic number by one, respectively. There are two types of beta decay: - **Beta-minus decay**: A neutron turns into a proton, emitting an electron and an antineutrino. The atomic number increases by 1 since a new proton is formed. - **Beta-plus decay**: A proton turns into a neutron, emitting a positron and a neutrino, decreasing the atomic number by 1. In the decay series exercise given, during a beta decay: - The atomic number of the nucleus rises by one. - For example, Radon-228 changes to Francium-228. Understanding beta decay is crucial because it acts as a counter mechanism to alpha decay, continually altering the nuclei of elements, which helps explain the variety of elements we see around us.

Thorium Decay Series

The thorium decay series is a series of radioactive decay reactions beginning with thorium-232 and ending in a stable isotope. The decay paths involve a combination of alpha and beta decays which gradually lead to the formation of stable lead isotopes. Here's how the series progresses: - **Begins with Thorium-232**: Undergoes successive alpha decay. - **Transformations**: Each transformation results in a different element with its own properties. - **Continues through various elements**: It includes elements like radium, radon, and eventually ends with lead. This series is significant in the study of radioactive substances and nuclear chemistry because it represents natural transmutations that occur over long periods. Thorium series is also immensely important in geological dating and tracing studies, helping scientists understand Earth's formation and the age of different rocks and minerals.