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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.

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