Question

The reaction \({ }_{5} \mathrm{~B}^{3} \longrightarrow{ }_{4} \mathrm{Be}^{8}+{ }_{1} \mathrm{e}^{0}\) takes place due to (a) \(\alpha\) decay (b) \(\beta\) decay (c) positron decay (d) electron capture

Short answer

The reaction takes place due to electron capture.

Step-by-step solution

Reaction Analysis

First, let's analyze the given nuclear reaction: \[{}_{5} ext{B}^{3} ightarrow {}_{4} ext{Be}^{8} + {}_{1} ext{e}^{0} \]The initial element is Boron (B) with an atomic number of 5, and the product is Beryllium (Be) with an atomic number of 4, along with an electron \({}_{1} ext{e}^{0}\).

Identify the Decay Process

Observe that the atomic number decreases from 5 in Boron to 4 in Beryllium. This indicates that a proton is being converted into a neutron. The presence of an electron (\({}_{1} ext{e}^{0}\)) in the products is key to identifying the type of decay.

Decide Type of Decay

Given that a proton is being converted into a neutron and an electron is present, the correct decay process is electron capture. In electron capture, an inner orbital electron is captured by the nucleus, which decreases the atomic number by one, turning a proton into a neutron.

Key concepts

Electron Capture

Electron capture is an intriguing process where an atomic nucleus captures one of its own electrons. Often, this electron comes from the innermost shell, known as the K-shell. This interaction allows the nucleus to convert a proton into a neutron. When this proton becomes a neutron, a significant transformation takes place.
The atomic number of the atom decreases by one, effectively altering the element's identity. However, the mass number, which is the sum of protons and neutrons, remains unchanged because we have simply reconfigured a proton into a neutron.
This process results in an electron neutrino being emitted from the nucleus due to the conservation of energy and momentum. Electron capture is essential in elements where it assists in achieving more stable nuclear configurations, typically in heavier elements where alternate decay processes might not be as energetically favorable.

• Nucleus captures an inner electron.
• Proton changes to a neutron.
• Atomic number decreases by 1.

Beta Decay

Beta decay is a common form of radioactive decay which involves the transformation of a neutron in the nucleus into a proton or vice versa. This process involves either beta minus ( ext{β}^-) or beta plus ( ext{β}^+) particles.
- **Beta-minus Decay:** This occurs when a neutron turns into a proton, emitting an electron and an antineutrino. As a result, the atomic number goes up by one, while the mass number stays the same. It often occurs in nuclei with an excess of neutrons. - **Beta-plus Decay (Positron Emission):** Here, a proton is changed into a neutron, releasing a positron and a neutrino. The atomic number decreases by one, making it similar to electron capture in terms of the atomic number change. However, it differs because the positron (an anti-electron) and a neutrino are emitted. This form of decay helps atoms with an excess of protons or neutrons stabilize by balancing forces within the nucleus. Beta decay is crucial to understanding the life cycle of elements and their transformations in nuclear reactions.

Nuclear Reaction Analysis

Nuclear reaction analysis is the process of understanding and evaluating what happens in a nuclear reaction. This analysis involves the study of changes in atomic numbers and mass numbers, which particles are emitted, and how energy and momentum conservation laws apply.
In our given problem, we identify the elements and isotopes involved. First, we note changes in the atomic number, which help us deduce the type of nuclear reaction. For example, a decrease in atomic number can suggest electron capture or beta-plus decay. Understanding the symbols, like {}_{5} ext{B}^{3} , which indicate boron with atomic number 5, and {}_{4} ext{Be}^{8} for beryllium, is important. Similarly, recognizing {}_{1} ext{e}^{0} indicates an electron is involved.

• Analyze changes in atomic and mass numbers.
• Identify particles involved (protons, neutrons, electrons).
• Apply conservation laws (energy and momentum).

Atomic Number Change

The atomic number represents the number of protons in an atom's nucleus. During nuclear reactions, this number can change, leading to transmutation, where one element turns into another. In our problem, boron initially has an atomic number of 5. Through the process, it changes to beryllium with an atomic number of 4.
Atomic number changes are crucial as they define the identity and properties of the element. In reactions like electron capture, a proton is turned into a neutron, causing the atomic number to decrease.
On the other hand, during beta decay processes: - **Beta-minus decay:** Atomic number increases by 1 because a neutron turns into a proton. - **Beta-plus decay (Positron emission):** Atomic number decreases by 1 as a proton turns into a neutron. Understanding these transitions is key to grasping nuclear chemistry, offering insights into how elements transform within stars, through radioactive decay, and within nuclear reactors.

• Represents number of protons.
• Changes define element identity.
• Crucial for nuclear chemistry insights.