Problem 62 - Chemistry A Molecular Approach

Question

Write the series of nuclear equations to represent the bombardment of Al- 27 with a neutron to form a product that subsequently undergoes a beta decay.

Step-by-Step Solution

Answer

The series of nuclear equations representing the bombardment of Al-27 with a neutron, followed by beta decay, is: \[ _{13}^{27}\text{Al} + _0^1n \rightarrow _{13}^{28}\text{Al} \] and \[ _{13}^{28}\text{Al} \rightarrow _{14}^{28}\text{Si} + _{-1}^0\beta \]

Step 1: Determine the Original Nucleus and Incident Particle

Identify the original nucleus and the incident particle involved in the nuclear reaction. Here, the original nucleus is Aluminum-27 (Al-27) and the incident particle is a neutron (n).

Step 2: Write the Equation for Neutron Capture

Aluminum-27 captures a neutron and becomes an unstable isotope. Write the nuclear equation for this process, which is \[ _{13}^{27}\text{Al} + _0^1n \rightarrow _{13}^{28}\text{Al} \]

Step 3: Identify the Type of Decay

Determine the type of decay the product undergoes. In this case, Aluminum-28 (Al-28) is unstable and undergoes beta decay.

Step 4: Write the Equation for Beta Decay

Write the nuclear equation for the beta decay of Aluminum-28. During beta decay, a neutron in the nucleus is transformed into a proton and a beta particle (an electron) is emitted. The atomic number increases by 1 while the mass number remains the same: \[ _{13}^{28}\text{Al} \rightarrow _{14}^{28}\text{Si} + _{-1}^0\beta \]

Key Concepts

Neutron Capture

Neutron capture is a nuclear reaction in which an atomic nucleus absorbs a neutron, becoming a heavier isotope of the same element. The process plays a crucial role in the creation of new isotopes and can trigger subsequent radioactive decay if the new isotope is unstable.

To better understand this, imagine a single neutron approaching a stable nucleus, like that of Aluminum-27. When Al-27 captures this neutron, it is transformed into an unstable isotope Aluminum-28, as represented by the equation:
\[_{13}^{27}Al + _{0}^{1}n \rightarrow _{13}^{28}Al\].

This absorption adds one to the mass number of the original nucleus, creating an isotope with greater mass, but leaving the atomic number unchanged as no protons are added to the nucleus during the process.

Beta Decay

Beta decay is one of the forms of radioactive decay where a beta particle, which is an electron, is emitted. This happens when an unstable nucleus seeks stability by converting a neutron into a proton while emitting an electron (beta particle) and an antineutrino.

In an equation, this process can be shown as:\[_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + _{-1}^{0}\beta\],where \( _{Z}^{A}X \) is the parent nucleus, \( _{Z+1}^{A}Y \) is the daughter nucleus, \( _{-1}^{0}\beta \) represents the beta particle, and \( Z \) and \( A \) represent the atomic number and mass number, respectively. For instance, in our example with Aluminum-28, the beta decay process would look like:\[_{13}^{28}Al \rightarrow _{14}^{28}Si + _{-1}^{0}\beta\].

This nuclear reaction results in an increase in atomic number by one, since a proton is added, but the mass number remains the same as before. The resultant nucleus, Silicon-28 in this case, is typically more stable than the original unstable nucleus.

Nuclear Reaction

A nuclear reaction involves the change in an atom's nucleus, usually by collision with another particle. The change can result in the transformation of elements or the change of one isotope to another. These reactions are critical for nuclear power generation and understanding nuclear stability.

Our example involving Aluminum-27 going through neutron capture and then beta decay encapsulates two nuclear reactions happening in a series:

• Neutron Capture: \(_{13}^{27}Al + _{0}^{1}n \rightarrow _{13}^{28}Al\)
• Beta Decay: \(_{13}^{28}Al \rightarrow _{14}^{28}Si + _{-1}^{0}\beta\)

Each step both alters the nucleus and signifies a distinct nuclear reaction, playing a part in the transmutation of elements. Nuclear reactions are governed by principles such as conservation of mass-energy and momentum.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but a different number of neutrons in the nucleus. This difference in neutron number results in variations of mass among the isotopes. While isotopes of an element share chemical properties, their nuclear properties, including stability, can vary significantly.

For example, \(_{13}^{27}Al\) and \(_{13}^{28}Al\) are isotopes of aluminum. They both have 13 protons, which defines them as aluminum in the periodic table, but Al-28 has one more neutron than Al-27. This additional neutron makes Al-28 unstable, leading to the beta decay process we discussed earlier. The transition between isotopes manifests in the realm of nuclear chemistry and physics, demonstrating uniqueness that extends beyond mere atomic weight differences.