Question

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine- \(17 .\)

Short answer

Fluorine-21 is likely to undergo beta-minus decay due to having more neutrons than protons. Fluorine-18 can achieve stability through beta-plus decay, aligning with the stable isotope Fluorine-19. Fluorine-17 can undergo either beta-plus decay to become Fluorine-18 or electron capture to become the stable Oxygen-17 isotope.

Step-by-step solution

1. Understand types of decay processes

There are mainly three types of decay processes: a. Alpha decay: In this process, a nucleus emits an alpha particle (consisting of 2 protons and 2 neutrons). b. Beta decay: This can be of two types, beta-minus decay and beta-plus decay. In beta-minus decay, a neutron is converted into a proton, while in beta-plus decay, a proton is converted into a neutron. c. Other decay processes: These include electron capture, gamma emission, etc.

2. Atomic composition of fluorine isotopes

First, let's find the atomic composition (number of protons and neutrons) of each fluorine isotope: - Fluorine-21: It has 9 protons and (21 - 9) = 12 neutrons. - Fluorine-18: It has 9 protons and (18 - 9) = 9 neutrons. - Fluorine-17: It has 9 protons and (17 - 9) = 8 neutrons.

3. Decay process for fluorine-21

Fluorine-21 has 12 neutrons and 9 protons. Having more neutrons than protons, this isotope can undergo beta-minus decay, where a neutron changes into a proton, resulting in neutron-neutron interactions to increase stability.

4. Decay process for fluorine-18

Fluorine-18 has 9 neutrons and 9 protons. Fluorine-19, the stable isotope, has 10 neutrons and 9 protons. To achieve stability, this isotope can undergo beta-plus decay, where a proton changes into a neutron, to increase neutron-proton interactions.

5. Decay process for fluorine-17

Fluorine-17 has 8 neutrons and 9 protons. This isotope can undergo beta-plus decay (proton changes to a neutron) to become the stable isotope fluorine-18 with 9 neutrons and 9 protons. Alternatively, it can undergo electron capture, where an electron is captured by the nucleus, changing a proton into a neutron and turning it into a stable oxygen-17 isotope with 8 protons and 9 neutrons. In conclusion, the likely decay processes for the given fluorine isotopes are: - Fluorine-21: Beta-minus decay - Fluorine-18: Beta-plus decay - Fluorine-17: Beta-plus decay or electron capture

Key concepts

Fluorine Isotopes

Fluorine isotopes are forms of the element fluorine, each differing by the number of neutrons in their atomic nuclei. The most common isotope of fluorine we encounter is fluorine-19, which is stable. Isotopes are variants of elements that possess the same number of protons but different numbers of neutrons. This difference alters their nuclear properties like stability and decay pathways. For fluorine:

• Fluorine-21 has 9 protons and 12 neutrons.
• Fluorine-18 has 9 protons and 9 neutrons.
• Fluorine-17 has 9 protons and 8 neutrons.

Suppose these isotopes are unstable, as is the case here. In that case, they will undergo radioactive decay, transforming into more stable elements over time. Understanding how each isotope might decay is crucial in understanding nuclear stability.

Beta Decay

Beta decay is a type of radioactive decay involving the transformation of an atomic nucleus. This process is characterized by one of two different transformations: beta-minus decay or beta-plus decay.

In beta-minus decay, a neutron is converted into a proton, with the emission of an electron (known as a beta particle) and an antineutrino. It typically occurs in isotopes with excess neutrons, such as fluorine-21. The result is an increase in the atomic number by one, transforming the element into a different one. For example, fluorine-21, with its excess of neutrons, might undergo beta-minus decay to become neon-21 with 10 protons.

Beta-plus decay, on the other hand, involves the conversion of a proton into a neutron, releasing a positron and a neutrino. Sometimes known as positron emission, this process decreases the atomic number by one. For fluorine isotopes like fluorine-18 and fluorine-17, beta-plus decay can occur, transforming them into more stable isotopes of oxygen or neon. This process allows these isotopes to achieve a more stable balance between protons and neutrons.

Electron Capture

Electron capture is another fascinating decay process that occurs in certain isotopes with a surplus of protons. In this process, an electron from an atom's inner shell is drawn into the nucleus, where it combines with a proton to form a neutron, emitting a neutrino.

This type of decay effectively reduces the atomic number by one without altering the atomic mass significantly. In terms of fluorine isotopes, electron capture can be a pathway for fluorine-17 to transform into the stable isotope oxygen-17, containing 8 protons and 9 neutrons.

Understanding electron capture is essential because it's a more passive form of decay compared to beta decay, occurring without the need to emit particles with charge. It often competes with beta-plus decay in isotopes where both pathways can potentially lead to stability.

Stable Isotopes

Stable isotopes are those that do not undergo radioactive decay over time. They have a balanced ratio of protons to neutrons, maintaining their integrity seemingly indefinitely. Fluorine-19 is a notable example of a stable isotope because it has 9 protons and 10 neutrons, an arrangement that does not lead to spontaneous transformation.

The concept of a stable isotope is crucial in the study of nuclear physics and chemistry because it defines what forms of an element remain unchanging. Understanding why an isotope like fluorine-19 is stable, while others like fluorine-21 are not, involves knowing about nuclear forces and the energy required to hold the nucleus together.

Identifying which isotopes are stable helps in numerous applications, from nuclear medicine using isotopic labeling to geological dating techniques. It underscores the importance of nuclear stability and its implications for both natural processes and human-derived technologies.