Question

Which one of the following particles is used to bombard \({ }_{13} \mathrm{Al}^{27}\) to give \({ }_{15} \mathrm{P}^{30}\) and a neutron? (a) \({ }_{1} \mathrm{H}^{2}\) (b) \(\gamma\) (c) \(\alpha\) (d) \(\beta\)

Short answer

{ }_{1} H^{2} (Deuterium).

Step-by-step solution

Write the nuclear reaction equation

To solve this problem, a nuclear reaction equation must be written including the target nucleus (Al^{27}_{13}), the particle that bombards the target, the resultant nucleus ({ }_{15} {P}^{30}), and the emitted particles such as a neutron in this case.

Apply conservation laws

The conservation of atomic number and mass number must be applied. For atomic number, the sum of the atomic numbers on the reactant side must equal the sum on the product side. Similarly, for the mass number, the sum of the mass numbers on the reactant side must equal the sum on the product side.

Identify the bombarding particle

Using the conservation laws, identify the particle that, when added to the target nucleus, leads to the formation of the resultant nucleus and the neutron.

Verify the options

Compare the identified particle from step 3 with the given options (a) H^{2}_{1} (Deuterium), (b) gamma, (c) ccc (Helium nucleus), and (d) neta (electron or positron).

Key concepts

Nuclear Chemistry

Nuclear chemistry is the study of changes that occur within the nuclei of atoms. This field of chemistry focuses on reactions that involve changes in nuclear structure, resulting in the transformation of one element into another. Such reactions release or absorb enormous amounts of energy that are significantly higher than in chemical reactions.

In the given exercise, we encounter a classic example of a nuclear reaction, where an aluminum nucleus is bombarded with a particle to produce phosphorus and a neutron. The bombardment causes a nuclear transformation, showcasing one of the fundamental processes studied in nuclear chemistry. This process, transmutation, is an artificial means of converting one element to another, a concept that plays a significant role in various applications, including medicine, energy production, and the study of fundamental particle interactions.

Conservation Laws in Nuclear Reactions

In nuclear reactions, conservation laws play a pivotal role, ensuring that certain properties remain unchanged. The two paramount conservation laws are the conservation of mass number and the conservation of atomic number.

The conservation of mass number states that the total mass number of the reactants must equal the total mass number of the products. On the other hand, atomic number conservation dictates that the total number of protons before the reaction must be the same as after the reaction.

Considering the given example, the sum of mass numbers and atomic numbers before and after the reaction reflect these laws. This is why they were utilized in the step-by-step solution to identify the correct bombarding particle. Adhering to these laws ensures that the nuclear reaction equation balances correctly, allowing us to reveal the particle involved in transforming aluminum into phosphorus while releasing a neutron.

Particles in Nuclear Reactions

Various particles can participate in nuclear reactions, playing roles as either projectiles that initiate the reactions, products of the reactions, or carriers of the forces within the atomic nucleus. Common particles encountered in nuclear reactions include alpha particles (\b\text{\(\balpha\b\text{\)}), beta particles (\b\text{\(\bbeta\b\text{\)}), neutrons (\b\text{\(bn\b\text{\)}), protons, and gamma rays (\b\text{\(\bgamma\b\text{\)}.

Each of these particles has unique properties that affect the reaction's outcome. For instance, alpha particles consist of 2 protons and 2 neutrons, beta particles are high-energy electrons or positrons, and gamma rays are high-energy photons. In the exercise, analyzing the properties of these particles against conservation laws guided us to identify the correct particle that, upon collision with aluminum, could yield phosphorus and a neutron.

Understanding the characteristics and behavior of these particles is crucial for predicting the result of a nuclear reaction, as well as in applications such as nuclear power generation and radiotherapy.