Question

Each of the following nuclides is known to undergo radioactive decay by production of a \(\beta\) particle, \({ }_{-1}^{0} \mathrm{e}\). Write a balanced nuclear equation for each process. a. \({ }^{136} \mathrm{I}\) \({ }^{53}\) b. \({ }_{51}^{133} \mathrm{Sb}\)

Short answer

a. The balanced nuclear equation for the beta decay of \(^{136}_{53}\mathrm{I}\) is: \[^{136}_{53}\mathrm{I} \rightarrow { }^{136}_{54}\mathrm{Xe} + { }_{-1}^{0} \mathrm{e} \] b. The balanced nuclear equation for the beta decay of \(^{133}_{51}\mathrm{Sb}\) is: \[^{133}_{51}\mathrm{Sb} \rightarrow { }^{133}_{52}\mathrm{Te} + { }_{-1}^{0} \mathrm{e} \]

Step-by-step solution

a. Finding the balanced nuclear equation for \(^{136}_{53}\mathrm{I}\) decay.

For beta decay, we know that a neutron is converted into a proton and an electron (\(\beta\)-particle) is released. Initially, we have \(^{136}_{53}\mathrm{I}\), and since a neutron is converted into a proton, we increase the atomic number by 1 while maintaining the same mass number. So, the new nuclide will have an atomic number of 53+1=54 and a mass number of 136. Using the periodic table, we can identify that the element with atomic number 54 is Xenon (Xe). Finally, we can write the balanced nuclear equation for the beta decay of \(^{136}_{53}\mathrm{I}\) as follows: \[^{136}_{53}\mathrm{I} \rightarrow { }^{136}_{54}\mathrm{Xe} + { }_{-1}^{0} \mathrm{e} \]

b. Finding the balanced nuclear equation for \(^{133}_{51}\mathrm{Sb}\) decay.

Now, we will find the balanced nuclear equation for the beta decay of \(^{133}_{51}\mathrm{Sb}\). Similar to part a, in the beta decay of \(^{133}_{51}\mathrm{Sb}\), a neutron is converted into a proton and an electron (\(\beta\)-particle) is released. Initially, we have \(^{133}_{51}\mathrm{Sb}\), and since a neutron is converted into a proton, we increase the atomic number by 1 while maintaining the same mass number. So, the new nuclide will have an atomic number of 51+1=52 and a mass number of 133. Using the periodic table, we can identify that the element with atomic number 52 is Tellurium (Te). Finally, we can write the balanced nuclear equation for the beta decay of \(^{133}_{51}\mathrm{Sb}\) as follows: \[^{133}_{51}\mathrm{Sb} \rightarrow { }^{133}_{52}\mathrm{Te} + { }_{-1}^{0} \mathrm{e} \]

Key concepts

Radioactive Decay

Radioactive decay is a natural process by which an unstable atomic nucleus loses energy by releasing radiation. It happens with different types of particles including alpha, beta, and gamma particles. This decay transforms the parent nuclide into a lighter daughter nuclide, making it more stable over time.

Key characteristics of radioactive decay include:

• Emission of energy: This includes radiation that can be hazardous in high doses.
• Conservation of mass and energy: While the exact form of an element might change, the total mass and energy remain constant.
• Random Process: Radioactive decay occurs at a random pace but can be statistically estimated using half-life.

In practical applications, radioactive decay plays a crucial role in energy production (nuclear power), medical treatments (radiotherapy), and scientific dating methods (carbon dating). Understanding this process is essential for handling radioactive materials safely and effectively.

Beta Decay

Beta decay is a specific type of radioactive decay where a beta particle, which is an electron or positron, is emitted from an atomic nucleus. This happens when a neutron in the nucleus transforms into a proton and an electron (or beta particle), which is then released. As a result, beta decay increases the atomic number by one but leaves the mass number unchanged.

Two principal forms of beta decay exist:

• Beta-minus decay (\( \beta^- \)): In this type, a neutron turns into a proton, and an electron is emitted.
• Beta-plus decay (\( \beta^+ \), or positron emission): Here, a proton converts into a neutron, releasing a positron.

Beta decay adjusts the properties of an atom, changing it from one element to another. Understanding this decay process helps in numerous scientific fields such as physics, chemistry, and biology, and is critical for applications in nuclear medicine.

Nuclear Equations

Nuclear equations are used to represent changes occurring in nuclear reactions, similar to how chemical equations represent chemical reactions. They demonstrate the transformation of initial reactants to end products, showing all changes in particles involved.

Key components to writing nuclear equations include:

• Nuclear symbols: These include the element symbol alongside its atomic and mass numbers.
• Balancing: Both the mass number and atomic number must be balanced on both sides of the equation.
• Particle notation: Particles like protons, neutrons, and electrons are represented in these equations.

For example, in the beta decay of \( ^{136}_{53} ext{I} \), the equation is \( ^{136}_{53} ext{I} \rightarrow ^{136}_{54} ext{Xe} + ^{0}_{-1} ext{e} \). This shows how an iodine atom changes to xenon while emitting a beta particle. Such equations are fundamental in understanding nuclear chemistry and predicting the behavior of radioactive substances.