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

Would it just be alpha-particle production, beta-particle production, gamma-ray production, and positron production for all of them?
How do i know which work for which?

http://www.arpansa.gov.au/basics/radioactivity.htm

19F has 9 protons and 10 neutrons.
F-21 would be above the band of stability. F-18 would be below the band of stability.

So F-21 would go through beta emission whereas F-18 and F-17 would go through either positron emission or electron capture?

I think those are safe bets.

Alpha-particle production is also possible for F-21, F-18, and F-17, but it is less likely than the other decay modes.

You are correct that the only stable isotope of fluorine is fluorine-19. When predicting the possible modes of decay for other isotopes of fluorine, there are a few factors to consider.

Fluorine-21 (F-21) has 9 protons and 12 neutrons, which puts it above the band of stability. It is likely to undergo beta decay, specifically beta-minus decay. In this process, one of the neutrons in the nucleus is converted into a proton, and a high-energy electron (beta particle) and an electron antineutrino are emitted.

Fluorine-18 (F-18) has 9 protons and 9 neutrons, placing it below the band of stability. It can undergo either positron emission or electron capture. Positron emission occurs when a proton in the nucleus is converted into a neutron, and a positron (antielectron) and an electron neutrino are emitted. Electron capture, on the other hand, involves the capture of an electron from the inner electron shell by a proton in the nucleus. This results in the emission of a neutrino.

Fluorine-17 (F-17) has 9 protons and 8 neutrons, which also places it below the band of stability. Similar to F-18, it can also undergo either positron emission or electron capture.

To summarize:
- F-21: Beta-minus decay
- F-18: Positron emission or electron capture
- F-17: Positron emission or electron capture

Please note that the actual decay modes can be influenced by additional factors, such as the energy difference between the initial and final states, nuclear spin, and availability of energy conservation pathways.

Yes, your predictions are correct. Fluorine-21 (F-21) would undergo beta decay, where a neutron in the nucleus is converted into a proton, emitting a beta particle (an electron) and an antineutrino. This process brings the atomic number up by one, resulting in oxygen-21.

On the other hand, both fluorine-18 (F-18) and fluorine-17 (F-17) are below the band of stability, meaning they have an excess of neutrons relative to protons. In order to achieve stability, they can undergo either positron emission or electron capture.

Positron emission occurs when a proton in the nucleus is converted into a neutron, emitting a positron and a neutrino. This reduces the atomic number by one. Therefore, F-18 could undergo positron emission to become oxygen-18.

Electron capture involves an electron from an inner orbital being captured by the nucleus, combining with a proton to form a neutron. This also reduces the atomic number by one. Consequently, F-17 could undergo electron capture to become oxygen-17.

In summary, F-21 would undergo beta decay, F-18 could undergo positron emission, and F-17 could undergo electron capture. It's important to note that these predictions are based on the principle of achieving a more stable configuration by reaching the nearest point on the band of stability.

For more detailed information, you can refer to the link you provided from the Australian Radiation Protection and Nuclear Safety Agency.