Question

Each of the following nuclides is known to undergo radioactive decay by production of a beta particle. Write a balanced nuclear equation for each process. a. \(\frac{55}{23} \mathrm{V}\) b. \(\frac{116}{47} \mathrm{Ag}\) c. \(\frac{229}{89} \mathrm{Ac}\)

Short answer

The balanced nuclear equations for the given processes are: a. \(\frac{55}{23} \mathrm{V} \rightarrow \, _{-1}^0 \beta + \overline{\nu} + \frac{55}{24} \mathrm{Cr}\) b. \(\frac{116}{47} \mathrm{Ag} \rightarrow \, _{-1}^0 \beta + \overline{\nu} + \frac{116}{48} \mathrm{Cd}\) c. \(\frac{229}{89} \mathrm{Ac} \rightarrow \, _{-1}^0 \beta + \overline{\nu} + \frac{229}{90} \mathrm{Th}\)

Step-by-step solution

Decay of \(\frac{55}{23} \mathrm{V}\)

For nuclide \(\frac{55}{23} \mathrm{V}\), when it undergoes beta decay, one neutron is converted into a proton. This increases the atomic number by one but keeps the mass number the same. Resulting nuclide: \(\frac{55}{24} \mathrm{Cr}\) Now, we can write the balanced nuclear equation: \[\frac{55}{23} \mathrm{V} \rightarrow \, _{-1}^0 \beta + \overline{\nu} + \frac{55}{24} \mathrm{Cr}\]

Decay of \(\frac{116}{47} \mathrm{Ag}\)

For nuclide \(\frac{116}{47} \mathrm{Ag}\), when it undergoes beta decay, one neutron is converted into a proton. This increases the atomic number by one but keeps the mass number the same. Resulting nuclide: \(\frac{116}{48} \mathrm{Cd}\) Now, we can write the balanced nuclear equation: \[\frac{116}{47} \mathrm{Ag} \rightarrow \, _{-1}^0 \beta + \overline{\nu} + \frac{116}{48} \mathrm{Cd}\]

Decay of \(\frac{229}{89} \mathrm{Ac}\)

For nuclide \(\frac{229}{89} \mathrm{Ac}\), when it undergoes beta decay, one neutron is converted into a proton. This increases the atomic number by one but keeps the mass number the same. Resulting nuclide: \(\frac{229}{90} \mathrm{Th}\) Now, we can write the balanced nuclear equation: \[\frac{229}{89} \mathrm{Ac} \rightarrow \, _{-1}^0 \beta + \overline{\nu} + \frac{229}{90} \mathrm{Th}\]

Key concepts

Radioactive Decay

Radioactive decay is a spontaneous process where unstable atomic nuclei release energy by emitting radiation. This natural phenomenon is central to understanding nuclear chemistry and is employed in various applications, from medical treatments to dating archaeological finds.

In these decay processes, an unstable element transforms into a more stable one. Types of radioactive decay include alpha decay, beta decay, and gamma decay, each involving different particles. In beta decay specifically, a neutron in the nucleus is converted into a proton—or vice versa—and a beta particle, which is an electron or positron, is emitted along with an antineutrino or neutrino.

Nuclear Chemistry

Nuclear chemistry is the study of changes that occur in atomic nuclei. It encompasses a wide array of processes, including radioactive decay, nuclear fission and fusion, and the synthesis of new elements. Nuclear chemistry is pivotal in applications that have substantial impacts on society, such as energy production, radiopharmaceuticals, and understanding the mechanisms of nuclear reactions.

Understanding how elements undergo radioactive decay helps us to predict the stability of nuclides, manage radioactive waste, and harness nuclear reactions for energy production. It allows scientists and engineers to devise applications that benefit humanity while maintaining safety protocols for handling radioactive materials.

Nuclear Equations

Nuclear equations are symbolic representations of nuclear reactions, showing the transformation of one set of nuclides to another. They are governed by the laws of conservation of mass number and atomic number, ensuring the equation is balanced on both sides. This means that the sum of the mass numbers (top numbers) and atomic numbers (bottom numbers) must be the same for the reactants and products.

For example, in beta decay, a neutron within the nucleus turns into a proton and emits a beta particle, usually represented as \( _{-1}^0 \beta \) or \( _{+1}^0 \beta \) for positron emission. By writing these equations, we can visualize and better understand the nuclear transmutation process, predicting the identities and properties of the nuclides produced.

Beta Particles

Beta particles are high-energy, high-speed electrons or positrons emitted during beta decay. There are two types of beta decay: beta-minus (\( \beta^- \)), where a neutron turns into a proton and emits an electron and an antineutrino; and beta-plus (\( \beta^+ \)), where a proton is converted into a neutron with the emission of a positron and a neutrino.

The emission of beta particles changes the nucleus's composition, leading to a new element with a different atomic number. This process is crucial in the medicinal field for treatments like radiotherapy, and it also helps us understand the pathways of elemental transformation in the universe. Intriguingly, beta particles can be harnessed in applications such as radiation therapy for treating cancer, showing the wider impact of this fundamental process.