Problem 53 - Chemistry Matter and Change

Question

Write a balanced nuclear equation for the beta decay of cesium-137.

Step-by-Step Solution

Answer

The balanced nuclear equation for the beta decay of cesium-137 is given by: \[ _{55}^{137}\textrm{Cs}\longrightarrow _{-1}^{0}\textrm{e} + _{56}^{137}\textrm{Ba} \]

Step 1: Understanding Beta Decay Process

Beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted from the nucleus of an unstable atom. In the process, a neutron is converted into a proton (if it's a beta minus decay) or a proton is converted into a neutron (if it's a beta plus decay). We will focus on beta minus decay in this exercise since it's the type of decay that occurs in cesium-137.

Step 2: Identifying the Initial Nucleus

Cesium-137 is represented as \(_{55}^{137}\textrm{Cs}\), where 55 is the atomic number (number of protons) and 137 is the mass number (sum of protons and neutrons). In this step, we identify the initial nucleus which is: \[ _{55}^{137}\textrm{Cs} \]

Step 3: Identifying the Beta Particle

In beta minus decay, an electron is emitted. This is represented as: \[ _{-1}^{0}\textrm{e} \] Remember that the atomic number of an electron is -1, and its mass number is 0.

Step 4: Identifying the Product Nucleus

In the beta minus decay of cesium-137, a neutron is converted into a proton, and an electron is emitted from the nucleus. This means that the atomic number increases by 1 (from 55 to 56) while the mass number remains the same (137). The product nucleus will be: \[ _{56}^{137}\textrm{X} \] Now, we just need to figure out which element has the atomic number 56, which is Barium (Ba).

Step 5: Writing the Balanced Nuclear Equation

Finally, we can write the balanced nuclear equation by showing the beta decay of cesium-137, emitting a beta particle (electron), and resulting in the production of barium-137: \[ _{55}^{137}\textrm{Cs}\longrightarrow _{-1}^{0}\textrm{e} + _{56}^{137}\textrm{Ba} \] This is the balanced nuclear equation for the beta decay of cesium-137.

Key Concepts

Beta Decay

Beta decay is one of the most interesting processes in nuclear physics. It's a type of radioactive decay where a beta particle, which can be either an electron or a positron, is emitted from an unstable atomic nucleus. In beta minus decay, which is our focus here, a neutron in the nucleus is transformed into a proton. This transformation increases the atomic number by one, as the creation of a new proton adds to the total proton count.

The emission of a beta particle offsets the increase in positive charge, maintaining electric neutrality. Importantly, the total mass number doesn't change; it remains constant because a proton is simply exchanged for an existing neutron, without adding or removing nucleons from the nucleus. Understanding this concept fully helps in predicting the resulting element after a beta decay process.

Cesium-137

Cesium-137 is a radioactive isotope of cesium with a mass number of 137. It's commonly represented as \(_{55}^{137}\mathrm{Cs}\)). This indicates it has 55 protons, and hence, an atomic number of 55.

Cesium-137 is well-known due to its use within the field of nuclear medicine and industrial processes. However, it is most notable for being a byproduct of nuclear reactors, contributing significantly to nuclear waste. It's crucial to comprehend the transformation it undergoes during beta decay. In the case of cesium-137, a neutron in its nucleus is converted into a proton, resulting in the formation of a new element with an atomic number 56 but retaining the same mass number of 137.

Cognizing the nature of cesium-137 and its transformation through beta decay can help understand nuclear waste management's importance and safety measures.

Radioactive Decay

Radioactive decay is a natural and spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. Over time, this decay process leads to the transformation of the atom into a different element or isotope. Among the different types of radioactive decay, which include alpha, beta, and gamma decay, beta decay is particularly common in isotopes like cesium-137.

During radioactive decay, elements approach a more stable state. The instability often arises when there are too many protons or neutrons within a nucleus. Releasing excess energy through decay alters the composition of the nucleus, leading to a potential change in the element itself.

Understanding radioactive decay, especially in isotopes like cesium-137 prone to beta decay, is fundamental for applications in energy production, medicine, and environmental science, as it provides insights into how long a radioactive substance will emit radiation and how it can be safely managed.