Question

Write a balanced nuclear equation for the reaction in which oxygen-15 undergoes positron emission.

Short answer

The balanced nuclear equation for the reaction in which oxygen-15 undergoes positron emission is given by: \[^{15}_{8}\)O -> \(^{15}_{7}\)N + \(^{0}_{1}\)e.

Step-by-step solution

Identify Isotopes and Particles: Oxygen-15 and Positron Emission

The initial isotope is Oxygen-15. Oxygen has an atomic number of 8 (denoted as Z) and a mass number of 15 (denoted as A). So, Oxygen-15 is represented by \(^{15}_{8}\)O. The emitted particle is a positron, a positively charged particle with the symbol e and the same mass as an electron but with a positive charge of +1. Positron is represented by \(^{0}_{1}\)e. Step 2: Determine the final isotope and balance the nuclear equation

Determine the final isotope and balance the nuclear equation

To find the final isotope after Oxygen-15 undergoes positron emission, we must subtract the atomic number of positron from the atomic number of Oxygen-15 and keep the mass number the same, since the mass number of the positron is 0. Final Isotope Atomic Number (Z) = 8 (oxygen) - 1 (positron) = 7 Final Isotope Mass Number (A) = 15 (oxygen) - 0 (positron) = 15 The final isotope has an atomic number of 7 and a mass number of 15, which corresponds to Nitrogen-15, represented by \(^{15}_{7}\)N. Now we can write the balanced nuclear equation: \(^{15}_{8}\)O -> \(^{15}_{7}\)N + \(^{0}_{1}\)e This balanced nuclear equation represents the reaction of Oxygen-15 undergoing positron emission.

Key concepts

Positron Emission

Positron emission is a type of radioactive decay observed in certain unstable isotopes. During this process, a proton in the nucleus of an atom is transformed into a neutron and a positively charged particle, known as a positron. The positron is identical to an electron, except it carries a positive charge. Let's explore its significance in nuclear reactions.

In our example involving Oxygen-15, this decay process helps to stabilize the nucleus by reducing the proton count, hence transforming the atom into another element. The emission is represented by the notation \( ^{0}_{1}\text{e} \), and when it occurs, the atomic number of the element decreases by one, while the mass number remains constant. This is because the positron itself has negligible mass and doesn't affect the total mass of the atoms involved in the reaction. Thus, the reaction must conserve both the charge and the number of nucleons (protons and neutrons), resulting in a different element with the same mass number.

Isotope Notation

Isotope notation provides a succinct way to express the identity of an atom, accounting for its number of protons and neutrons. Every isotope can be represented using its chemical symbol, with two important numbers:

The atomic number (Z) which is located at the lower left of the symbol and denotes the number of protons, and the mass number (A) at the upper left, indicating the sum of protons and neutrons. For instance, Oxygen-15 is denoted as \( ^{15}_{8}\text{O} \), specifying an oxygen isotope with 8 protons and 7 neutrons. Understanding isotope notation is crucial for students as it allows them to quickly identify the composition of the nucleus and predict how an isotope may undergo radioactive decay.

Nuclear Reactions

A nuclear reaction involves the transformation of one or more atomic nuclei. Unlike chemical reactions that involve the exchange of electrons, nuclear reactions are changes that take place within the nucleus and typically result in the alteration of atomic numbers and mass numbers of the involved atoms.

In such reactions, including the positron emission from Oxygen-15, the conservation laws are key. Both mass and atomic numbers must be conserved. This is why, after Oxygen-15 (\( ^{15}_{8}\text{O} \)) emits a positron (\( ^{0}_{1}\text{e} \)), it transforms into Nitrogen-15 (\( ^{15}_{7}\text{N} \)), maintaining the balance of mass and atomic number totals on both sides of the equation. Students should focus on applying these conservation laws to predict the products of nuclear reactions and to ensure the balance of the nuclear equations they write.