Problem 41 - Chemistry The Molecular Science

Question

Nitrogen-13, a diagnostic radioisotope used to detect tumors, is made by reaction of oxygen- 16 with a proton. An alpha particle is also produced in addition to nitrogen-13. Write a balanced nuclear equation to represent this process.

Step-by-Step Solution

Answer

The balanced equation is \(^8_{16}O + ^1_1p \rightarrow ^7_{13}N + ^4_2He\).

Step 1: Identify the Nuclides Involved

We know that Oxygen-16 reacts with a proton to produce Nitrogen-13 and an alpha particle. Let's write down the symbols: Oxygen-16 \(^8_16O\), proton \(^1_1p\), Nitrogen-13 \(^7_{13}N\), and alpha particle \(^4_2He\).

Step 2: Write the Nuclear Equation

Write the nuclear equation based on the given information: \[^8_{16}O + ^1_1p \rightarrow ^7_{13}N + ^4_2He\].

Step 3: Verify Mass Number Conservation

Check if the sum of the mass numbers on both sides of the equation is equal. On the left, it's 16 (oxygen) + 1 (proton) = 17. On the right, it's 13 (nitrogen) + 4 (alpha particle) = 17. The mass number is conserved.

Step 4: Verify Atomic Number Conservation

Check if the sum of the atomic numbers on both sides of the equation is equal. On the left, it's 8 (oxygen) + 1 (proton) = 9. On the right, it's 7 (nitrogen) + 2 (alpha particle) = 9. The atomic number is also conserved.

Key Concepts

Radioisotopes

Radioisotopes are isotopes of elements that have an unstable nucleus. This instability causes them to undergo radioactive decay, releasing energy in the form of particles or electromagnetic waves, as they transition to a more stable state. Radioisotopes play a crucial role in various fields like medicine, industry, and research. For example, in medicine, they are used in diagnosis and treatment of diseases. In the exercise you looked at earlier, Nitrogen-13 is a radioisotope used in diagnostic imaging to detect tumors.
It has a relatively short half-life, allowing it to decay quickly enough to be useful in these medical imaging techniques without leaving lingering radiation in the body. Key points about radioisotopes include:

• Unstable nuclei that seek stability through decay.
• Ability to emit various types of radiation: alpha, beta, and gamma.
• Widely used in medical, industrial, and scientific applications.
• Half-life determines how long the radioisotope remains active.

Understanding how these isotopes behave and interact helps in creating more effective uses in technology and healthcare.

Alpha Particles

Alpha particles are a type of radiation emitted during the radioactive decay of certain unstable nuclei, like those of heavy elements. They consist of two protons and two neutrons, which is the same composition as a helium nucleus.
This similarity is why alpha particles are often denoted as \[^4_2He\]. These particles have a relatively high mass and a positive charge due to the presence of protons. In the nuclear equation in the exercise, an alpha particle is one of the products, demonstrating its role in transforming the original nuclide into a more stable form. Here are some key characteristics of alpha particles:

• Consist of two protons and two neutrons.
• Have a +2 charge because they have two protons with positive charges.​
• Relatively high mass compared to other types of radioactive emissions.
• Low penetration power, can be stopped by a sheet of paper.

This low penetration ability is why alpha particles are considered relatively low-risk outside the body but can be harmful if ingested or inhaled.

Mass Number Conservation

Mass number conservation is a fundamental concept in nuclear reactions. It states that the total mass number – which is the sum of protons and neutrons in an atomic nucleus – must remain the same before and after a nuclear reaction.
This conservation is essential for balancing nuclear equations and ensuring the integrity of the reaction process. In the example you saw, Oxygen-16 and a proton react together resulting in Nitrogen-13 and an alpha particle. Checking for mass number conservation involves adding the mass numbers on each side of the equation:

• On the reactant side: \(16 + 1 = 17\)
• On the product side: \(13 + 4 = 17\)

These sums are identical, showing that mass number conservation holds true. This principle ensures that matter remains consistent throughout nuclear reactions, helping validate the accuracy of the equation written. Additionally, understanding mass number conservation helps predict the outcomes of nuclear reactions accurately.