Question

Write the balanced nuclear equation for the induced transmutation of aluminum-27 into sodium-24 by neutron bombardment. An alpha particle is released in the reaction.

Short answer

The balanced nuclear equation for the induced transmutation of aluminum-27 into sodium-24 by neutron bombardment, with an alpha particle released in the reaction is: \( _{13}^{27}\textrm{Al} + _{0}^{1}\textrm{n} \rightarrow _{11}^{24}\textrm{Na} + _{2}^{4}\textrm{α} \)

Step-by-step solution

Identify the Elements and Particles

First, let's identify the elements and particles involved in this nuclear reaction: 1. Aluminum-27 (Al-27) represents aluminum isotope with a mass number of 27. 2. Neutron bombardment means that a neutron (n) is bombarding the aluminum-27. 3. The product is sodium-24 (Na-24) with a mass number of 24. 4. An alpha particle (α) is released during the reaction. We also need the atomic numbers of Aluminum (Al) and Sodium (Na). Aluminum (Al) has an atomic number of 13. Sodium (Na) has an atomic number of 11.

Write the Unbalanced Nuclear Equation

Now let's write an unbalanced nuclear equation involving these particles and elements: \( _{13}^{27}\textrm{Al} + _{0}^{1}\textrm{n} \rightarrow _{11}^{24}\textrm{Na} + _{2}^{4}\textrm{α} \)

Balance the Nuclear Equation

To balance the nuclear equation, we need to make sure that both the atomic numbers (subscripts) and the mass numbers (superscripts) are conserved during the reaction. For atomic numbers: - On the left side: 13 (Aluminum) + 0 (neutron) = 13 - On the right side: 11 (Sodium) + 2 (alpha particle) = 13 For mass numbers: - On the left side: 27 (Aluminum) + 1 (neutron) = 28 - On the right side: 24 (Sodium) + 4 (alpha particle) = 28 Since both the atomic numbers and mass numbers are conserved, the nuclear equation is balanced. So, the balanced nuclear equation for the induced transmutation of aluminum-27 into sodium-24 by neutron bombardment, with an alpha particle released in the reaction is: \( _{13}^{27}\textrm{Al} + _{0}^{1}\textrm{n} \rightarrow _{11}^{24}\textrm{Na} + _{2}^{4}\textrm{α} \)

Key concepts

Nuclear Reaction

A nuclear reaction involves changes in an atom's nucleus and often includes the transformation of one element into another.

During a nuclear reaction, particles within the nuclei, such as protons and neutrons, get rearranged or combined to form new elements and isotopes. This process can be natural or induced, such as by bombarding the nucleus with particles.

In the example provided, neutron bombardment induces a change in an aluminum nucleus, resulting in the production of a different element, sodium, and an alpha particle. This type of reaction is not only fundamental to understanding nuclear chemistry but also has practical applications in medicine, energy production, and material science.

Neutron Bombardment

Neutron bombardment is a type of nuclear reaction in which a target nucleus is hit by free neutrons. Neutrons are chosen because they are electrically neutral, meaning they can penetrate the nucleus without being repelled by the protons that are positively charged.

In neutron bombardment reactions, like the transmutation of aluminum to sodium, a neutron is captured by the nucleus of the target atom, which leads to a reaction that can produce different isotopes or even different elements.

Alpha Particle

An alpha particle is a type of nuclear particle consisting of two protons and two neutrons bound together. This is the same as the nucleus of a helium-4 atom.

Alpha particles are emitted during various radioactive decay processes and certain nuclear reactions, including the one in question where an alpha particle is released when aluminum-27 is bombarded by a neutron to form sodium-24. Alpha particles have significant biological effects when they interact with living tissue, which is why they are heavily studied in nuclear physics and medicine.

Conservation of Mass Number

In nuclear reactions, the conservation of mass number is crucial for balancing nuclear equations. The mass number is the total number of protons and neutrons in a nucleus. When a nuclear reaction occurs, the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products.

In the provided exercise, the sum of the mass numbers on the reactant side (aluminum-27 plus the neutron) equals 28, which is the same total when we add the mass numbers of the resulting sodium-24 and the alpha particle on the product side. Thus, the conservation of mass number is observed in this nuclear transmutation.

Conservation of Atomic Number

The conservation of atomic number dictates that the total number of protons must remain the same before and after a nuclear reaction.

Protons define the identity of an element, and during nuclear reactions, even though neutrons and protons may be rearranged and emitted, the number of protons must be conserved to maintain charge balance. In our example, the atomic number starts with 13 (from aluminum) and adds 0 (since neutrons do not contribute). After the reaction, we have 11 (from sodium) plus 2 (from the two protons in the alpha particle), resulting in the same total atomic number of 13, thus fulfilling the conservation of atomic number.