Question

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

Short 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-by-step solution

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.

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: \[ _{55}^{137}\textrm{Cs} \]

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.

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).

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.