You would have to find out what the cross-section is for the particular alpha-capture reaction. Then you can find out a nuclear reaction rate. At terrestrial temperatures, the alpha-capture rate is going to be small, but non-negligible.
Presumably the question is targeted at whether the products of an alpha-capture are dangerous, so we need to investigate the products of nuclear reactions on a case-by-case basis.
Most aluminium is in the form of stable $\displaystyle ^{27}$Al, so we have $\displaystyle ^{27}$Al($\displaystyle \alpha, \gamma$)$\displaystyle ^{31}$P, $\displaystyle ^{31}$P is stable, so it's safe. It's probably going to be the dominant reaction as well.
We also have $\displaystyle ^{27}$Al($\displaystyle \alpha, n$)$\displaystyle ^{30}$P. $\displaystyle ^{30}$P is unstable ($\displaystyle \beta^+$ decay) with a half-life of 2.5 minutes, so that could be dangerous if you're close to it.
A sample of aluminium will have a small amount of $\displaystyle ^{26}$Al, so there's also the possibility of $\displaystyle ^{26}$Al($\displaystyle \alpha, \gamma$)$\displaystyle ^{30}$P, so it seems that there's a chance that you're going to get some radioactive $\displaystyle ^{30}$P.
EDIT: The gamma rays and neutrons from the reactions might be harmful too, but I'm not sure without looking into the energetics of it, which could take a while!
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Last edited by benit13; Mar 29th 2018 at 02:48 AM.
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