Question

Which of the following statements best explains why alpha emission is relatively common, but proton emission is extremely rare? \begin{equation}\begin{array}{l}{\text { (a) Alpha particles are very stable because of magic numbers }} \\ \quad {\text { of protons and neutrons. }} \\\ {\text { (b) Alpha particles occur in the nucleus. }} \\ {\text { (c) Alpha particles are the nuclei of an inert gas. }} \\ {\text { (d) An alpha particle has a higher charge than a proton. }}\end{array}\end{equation}

Short answer

(a) Alpha particles are very stable because of magic numbers of protons and neutrons.

Step-by-step solution

Recognize the key concepts

Alpha emission is a type of radioactive decay characterized by the release of an alpha particle (composed of 2 protons and 2 neutrons, equivalent to a helium-4 nucleus) from an unstable nucleus. On the other hand, proton emission is another type of radioactive decay that occurs when a proton is ejected from a highly unstable nucleus. Now, let's examine each of the provided statements to find the best explanation.

Evaluate statement (a)

Alpha particles are very stable because of magic numbers of protons and neutrons: An alpha particle has 2 protons and 2 neutrons, and both the numbers of protons and neutrons are considered as "magic numbers" because they have a higher stability resulting from completely filled nuclear shells. This statement is promising.

Evaluate statement (b)

Alpha particles occur in the nucleus: Although alpha particles are found in the nucleus, this fact does not explain why alpha emission is more common than proton emission. Therefore, this statement is not the best explanation.

Evaluate statement (c)

Alpha particles are the nuclei of an inert gas: Though it is true that alpha particles are equivalent to the nucleus of a helium-4 atom (an inert gas), this fact is not sufficient to explain why alpha emission is more common than proton emission.

Evaluate statement (d)

An alpha particle has a higher charge than a proton: This statement simply compares the charges of an alpha particle and a proton without explaining why alpha emission is more common. Therefore, this statement is not the best explanation. Based on the analysis of each statement, it is evident that statement (a) is the best explanation for the given exercise. So, the correct answer is: (a) Alpha particles are very stable because of magic numbers of protons and neutrons.

Key concepts

Radioactive Decay

Radioactive decay is a natural process by which an unstable atomic nucleus loses energy by emitting radiation. This process results in the transformation of the original nucleus into a different state, often a different element. There are various types of radioactive decay:

• Alpha decay: The nucleus emits an alpha particle, which consists of two protons and two neutrons. This results in the transformation of the original atom into a nucleus with two fewer protons and two fewer neutrons.
• Beta decay: Emission of a beta particle (an electron or positron), changing a neutron into a proton, or vice versa.
• Gamma decay: The nucleus drops to a lower energy state by emitting a gamma photon, a form of electromagnetic radiation.
• Proton emission: Although rare, certain highly unstable nuclei can emit a proton directly.

The type of decay a nucleus undergoes depends on the energy dynamics and what will allow it to transform into a more stable configuration.

Nuclear Stability

Nuclear stability refers to the ability of a nucleus to remain unchanged over time. A stable nucleus does not emit particles spontaneously. However, many factors influence nuclear stability:

• Proton-to-neutron ratio: A balanced ratio aids in nuclear stability. Too many protons or neutrons cause repulsion and instability.
• Nuclear forces: Strong nuclear forces hold the protons and neutrons together, overcoming electrostatic repulsion between protons.
• Binding energy: The energy required to break a nucleus into its constituent protons and neutrons. Higher binding energy indicates greater stability.

For a nucleus to retain its stability, it must possess an optimal combination of these factors. Otherwise, it may undergo radioactive decay to achieve a more stable state.

Magic Numbers

Magic numbers are specific numbers of nucleons (protons or neutrons) that result in highly stable atomic configurations. When the number of protons or neutrons in a nucleus corresponds to these magic numbers, the nucleus is exceptionally stable. These numbers are usually:

• 2,
• 8,
• 20,
• 28,
• 50,
• 82 for protons, and
• 126 for neutrons.

Magic numbers are linked to the shell model of the nucleus, akin to electron configurations in atoms, where complete shells of nucleons lead to optimal stability. Alpha particles, comprising 2 protons and 2 neutrons (both magic numbers), are thus very stable, making alpha decay more common.

Proton Emission

Unlike alpha emission, proton emission is a rare form of radioactive decay. It involves the release of a single proton from a highly unstable nucleus. Several factors contribute to this rarity:

• Proton Barrier: The strong nuclear force opposes the emission of just one proton, demanding higher energy to overcome this barrier.
• Instability Requirement: Nuclei that emit protons are often extremely neutron-deficient, which is less common.
• Energy Considerations: Emission requires an energy profile that results in overall greater stability, which isn't always achieved easily with proton emission.

While it does occur in certain isotopes far from stability, other forms of decay like alpha emission are more efficient in permitting the nucleus to achieve stability.