Question

Each of the following nuclides is known to undergo radioactive decay by production of an alpha particle. Write a balanced nuclear equation for each process. a. \(\frac{227}{90} \mathrm{Th}\) b. \(\frac{211}{83} \mathrm{Bi}\) c. \(\frac{244}{96} \mathrm{Cm}\)

Short answer

The balanced nuclear equations for the alpha decay of the given nuclides are: a. \(\frac{227}{90} \mathrm{Th} \rightarrow \frac{223}{88} \mathrm{Ra} + \frac{4}{2}\mathrm{He}\) b. \(\frac{211}{83} \mathrm{Bi} \rightarrow \frac{207}{81} \mathrm{Tl} + \frac{4}{2}\mathrm{He}\) c. \(\frac{244}{96} \mathrm{Cm} \rightarrow \frac{240}{94} \mathrm{Pu} + \frac{4}{2}\mathrm{He}\)

Step-by-step solution

a. Thorium-227 alpha decay equation

Given the radioactive nuclide Thorium-227 \(\left(\frac{227}{90} \mathrm{Th}\right)\), we need to determine the resulting nucleus after the emission of an alpha particle. The alpha particle can be represented as \(\frac{4}{2}\mathrm{He}\). The equation for the decay process is: \[\frac{227}{90} \mathrm{Th} \rightarrow \text{Daughter nucleus} + \frac{4}{2}\mathrm{He}\] Now, we need to balance the nuclear equation by making sure the total number of nucleons (mass number) and protons (atomic number) is the same on both sides. The mass of the daughter nucleus will be: Mass = 227 - 4 = 223. The atomic number (protons) of the daughter nucleus will be: Atomic number = 90 - 2 = 88. The resulting nuclide will be \(\frac{223}{88} \mathrm{Ra}\) (Radium). Thus, the balanced equation for the alpha decay of Thorium-227 is: \[\frac{227}{90} \mathrm{Th} \rightarrow \frac{223}{88} \mathrm{Ra} + \frac{4}{2}\mathrm{He}\]

b. Bismuth-211 alpha decay equation

Given the radioactive nuclide Bismuth-211 \(\left(\frac{211}{83} \mathrm{Bi}\right)\), we need to determine the resulting nucleus after the emission of an alpha particle. The alpha particle can be represented as \(\frac{4}{2}\mathrm{He}\). The equation for the decay process is: \[\frac{211}{83} \mathrm{Bi} \rightarrow \text{Daughter nucleus} + \frac{4}{2}\mathrm{He}\] Now, we need to balance the nuclear equation by making sure the total number of nucleons (mass number) and protons (atomic number) is the same on both sides. The mass of the daughter nucleus will be: Mass = 211 - 4 = 207. The atomic number (protons) of the daughter nucleus will be: Atomic number = 83 - 2 = 81. The resulting nuclide will be \(\frac{207}{81} \mathrm{Tl}\) (Thallium). Thus, the balanced equation for the alpha decay of Bismuth-211 is: \[\frac{211}{83} \mathrm{Bi} \rightarrow \frac{207}{81} \mathrm{Tl} + \frac{4}{2}\mathrm{He}\]

c. Curium-244 alpha decay equation

Given the radioactive nuclide Curium-244 \(\left(\frac{244}{96} \mathrm{Cm}\right)\), we need to determine the resulting nucleus after the emission of an alpha particle. The alpha particle can be represented as \(\frac{4}{2}\mathrm{He}\). The equation for the decay process is: \[\frac{244}{96} \mathrm{Cm} \rightarrow \text{Daughter nucleus} + \frac{4}{2}\mathrm{He}\] Now, we need to balance the nuclear equation by making sure the total number of nucleons (mass number) and protons (atomic number) is the same on both sides. The mass of the daughter nucleus will be: Mass = 244 - 4 = 240. The atomic number (protons) of the daughter nucleus will be: Atomic number = 96 - 2 = 94. The resulting nuclide will be \(\frac{240}{94} \mathrm{Pu}\) (Plutonium). Thus, the balanced equation for the alpha decay of Curium-244 is: \[\frac{244}{96} \mathrm{Cm} \rightarrow \frac{240}{94} \mathrm{Pu} + \frac{4}{2}\mathrm{He}\]

Key concepts

Nuclear Equations

Nuclear equations are essential tools in understanding and representing nuclear reactions. Unlike regular chemical equations, nuclear equations focus on the changes within the atom's nucleus. These equations are used to depict processes such as nuclear decay, fission, and fusion, where the identity of atoms changes. For instance, in nuclear decay, an unstable nucleus releases particles to become more stable, leading to a new element formation.
Let's look at alpha decay as an example. This process involves the emission of an alpha particle, which is equivalent to a helium nucleus (\( \frac{4}{2}\mathrm{He} \)). Writing nuclear equations for alpha decay involves identifying the original nuclide, determining the emitted alpha particle, and calculating the resulting daughter nuclide.
To write these equations:

• Identify the parent nucleus and the emitted alpha particle.
• Apply the conservation of nucleons and protons, ensuring both sides of the equation balance.
• Determine and write the daughter nucleus.

Balancing nuclear equations helps us understand the transformation that occurred during the decay process.

Radioactive Decay

Radioactive decay is a spontaneous process where an unstable atomic nucleus releases energy by emitting particles. This emission transforms the original atom into a more stable atom, often changing its elemental identity. Radioactive decay can occur through different modes like alpha, beta, or gamma decay, each varying based on the particles emitted.
Alpha decay specifically involves the release of alpha particles, which are composed of 2 protons and 2 neutrons (a helium nucleus). This type of decay reduces the atomic number by 2 and the mass number by 4 in the original nucleus. As it happens naturally, alpha decay is used in scientific fields for dating rocks and understanding nuclear properties.
Recognizing radioactive decay and its types is crucial in predicting the behavior of radioactive elements. It illustrates how elements transmute in nature, resulting in the formation of different substances.

Balanced Equations

Balanced equations are fundamental in nuclear chemistry. They ensure matter conservation, meaning that the same number of subatomic particles is present in both the reactants and products. In nuclear equations, this means that the sum of mass numbers (total nucleons) and the sum of atomic numbers (protons) are equal on both sides of the equation.
To balance a nuclear equation, one should:

• Check the mass numbers of the original nucleus and any emitted particles.
• Ensure that the product side has the same total mass number and atomic number as the reactant side.
• Adjust for particles like alpha particles in specific decays to maintain balance.

By mastering balanced equations, you can effectively depict nuclear reactions. This helps in predicting the products and understanding stability changes in nuclides during radioactive decay.