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If you had the power to transmute any element you touch into one of the two immediately adjacent to it on the periodic table by adding or removing one proton and you tried using it on the silicon in dirt/bedrock to create white phosphorus, what would happen? Would the transmuted earth immediately react with the air and ignite like I want, or would the effects be weirder/less useful?

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Nope ... as sorry I am to disappoint you, thing is, it would not immediately turn ablaze because silicon is not found in free state in the soil, but rather as dioxide (SiO$_2$).

Phosphorous ignites in air to form pentoxide (P$_2$O$_5$). So while silicon converted into phosphorous would not be completely saturated with oxygen already, it is hard to say if it would ignite instantaneously or would it rather be a slow (spanning several minutes at least, if not hours) oxidation reaction.

If you are keen to turn things on fire with touch, you would have more luck with sulfur instead. Since it is easily available and is cheap, you can just keep some of it handy in your pocket and convert it into pure phosphorous and turn it ablaze any time.

Also, although unrelated to your question, I might remind you that there is a little fallacy in your world. The wizards of your world would be able to turn any element into any other element as they see fit, not just one element before or after in the periodic table. The reason being, that they can continue to deduct or add protons (and neutrons) with their touch until they obtain the element of their choice. If they can do this once (convert an element to previous or next element), they can keep doing this over and over again with the converted element(s).

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  • $\begingroup$ Assuming the new element was not a gas and then goes away before the next transformation is performed. Darn those noble gasses, messing up everything! $\endgroup$ – Mark Ripley Sep 23 '16 at 5:35
  • $\begingroup$ As an alternate solution, Z. Schoeder might be able to avoid the fallacy you mention by having the atoms "remember" what they were originally and only support transmutation within the window of +/- 1 proton. That doesn't challenge your point about atomic structures (though it does bring up the question of what chemistry happens when you suddenly make something very unstable by changing its atoms) $\endgroup$ – Cort Ammon Sep 23 '16 at 16:07
  • $\begingroup$ @CortAmmon: Does atomic memory exist? Even in fiction ... If that be the case, then the converted atoms would not be "normal" atoms and would depict some really wonderful and bizarre characteristics with regard to their memory skills :p I'd love to know scientists have found such atoms :D $\endgroup$ – Youstay Igo Sep 24 '16 at 3:27
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Keep in mind that the variation in number of protons is not the only change between Si and P.

The most common form of Si is 28Si which has 14 protons, 14 neutrons, and 14 electrons (in non-ionic form).
The most common form of P is 31P which has 15 protons, 16 neutrons, and 15 electrons (in non-ionic form).

So in addition to adding a proton you'd also need to come up with 2 neutrons and an electron (which might be capture-able from the environment). There's no known isotope of P with only 14 neutrons. Such an element would almost certainly have a very short radioactive half life and decay into 29Si (through beta emission of a positron, thus converting a proton into a neutron). There is 30Si which has 16 neutrons, it would be much more amenable to conversion to P but it also only makes up 3% of Si in general.

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