Problem 15 - Chemistry Matter and Change

Question

Predict the nuclear equation for the alpha decay of radium-226 used on the tips of older lightning rods.

Step-by-Step Solution

Answer

The nuclear equation for the alpha decay of radium-226 used in older lightning rods is: \(_{88}^{226}\textrm{Ra} \rightarrow _{86}^{222}\textrm{Rn} + _{2}^{4}\textrm{He}\) This means that radium-226 undergoes alpha decay, emitting an alpha particle, to form radon-222.

Step 1: Identify the initial atom and its isotopes

Firstly, we need to identify the isotope of radium that needs to undergo alpha decay. Radium has multiple isotopes, but in this case, we are dealing with radium-226. An isotope is represented by \(A_{Z}X\), where A is the mass number (the total number of protons and neutrons), Z is the atomic number (the number of protons), and X is the chemical symbol. Radium-226 is represented as: \(_{88}^{226}\textrm{Ra}\)

Step 2: Determine the components of the alpha particle

An alpha particle is a helium nucleus, which consists of 2 protons and 2 neutrons. It is represented by the chemical symbol He and has a mass number (A) of 4 and an atomic number (Z) of 2. An alpha particle is represented as: \(_{2}^{4}\textrm{He}\)

Step 3: Write the nuclear equation for alpha decay

In an alpha decay process, the radium-226 atom emits an alpha particle, causing the remaining atom to transform into a different element with a lower atomic mass and atomic number. To find the element and its isotope formed after the decay, we need to subtract the mass and atomic number of the alpha particle from those of radium-226: Remaining Mass Number (A): 226 - 4 = 222 Remaining Atomic Number (Z): 88 - 2 = 86 The resulting atom will have a mass number of 222 and an atomic number of 86. This corresponds to the chemical element Radon (Rn). The nuclear equation for the alpha decay of radium-226 is: \(_{88}^{226}\textrm{Ra} \rightarrow _{86}^{222}\textrm{Rn} + _{2}^{4}\textrm{He}\) This equation means that radium-226 undergoes alpha decay to form radon-222 and an alpha particle.

Key Concepts

Nuclear Equation

A nuclear equation represents a nuclear reaction, much like a chemical equation represents a chemical reaction. It shows the transformation of one element into another by illustrating changes in the nucleus. In the case of alpha decay, a parent nucleus emits an alpha particle, resulting in a new nucleus with a reduced atomic mass and number.

• The left side of the equation represents the original nucleus.
• The right side shows the resulting nucleus and the emitted particle.

The overall mass and charges remain balanced. For instance, during the decay of radium-226, the nuclear equation is written as: \[ _{88}^{226}\textrm{Ra} \rightarrow _{86}^{222}\textrm{Rn} + _{2}^{4}\textrm{He} \] This means that radium-226 transforms into radon-222 and a helium nucleus. The total number of protons and neutrons is conserved, emphasizing the law of conservation of mass and charge.

Radium-226

Radium-226 is a radioactive isotope of radium, known for its instability and radioactive decay. It has an atomic number of 88, meaning it contains 88 protons, and a mass number of 226, indicating a total of 226 protons and neutrons. Radium-226 decays by emitting an alpha particle, a process that changes it into a different element while releasing radiation.
Radium-226 was historically used in items like lightning rods and luminous paints, but due to its radioactivity, safer alternatives are now preferred.

• Atomic Number (Z) = 88
• Mass Number (A) = 226

Its presence is natural, primarily found in uranium ores. Its decay leads to other radioactive elements until stability is reached.

Helium Nucleus

An alpha particle is essentially a helium nucleus, consisting of 2 protons and 2 neutrons. Its representation in nuclear equations is crucial as it shows what is emitted during nuclear decay.In the nuclear equation, a helium nucleus is depicted as:\[ _{2}^{4}\textrm{He} \] The mass number (A) is 4, accounting for the total protons and neutrons, while the atomic number (Z) is 2, representing the protons alone. The emission of a helium nucleus is responsible for the change in the original element, hence altering not only atomic structure but also the element itself.This small particle plays a significant role in nuclear chemistry, driving the transformation of materials and their properties.

Radon-222

Radon-222 is the daughter product of the alpha decay of radium-226. It is a colorless, odorless gas that is also radioactive. Like its precursor, it is radioactive but significantly different in its properties.

• Atomic Number (Z) = 86
• Mass Number (A) = 222

Upon decay, radium-226 loses an alpha particle, and the resulting radon-222 inherits 86 protons and 222 as its total for protons and neutrons. Radon-222 is a noble gas, which means it doesn't readily react with other materials. However, being radioactive, it poses health risks, especially in poorly ventilated areas. Understanding its presence, especially in homes, is important as it can accumulate and lead to health issues over time.