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Edit: Everyone's ignoring the condition that the wizard needs to survive! This transmutation is to an object they're holding, it is not at a distance and any shielding is on the object and gets transmuted also.

This is a modern wizard who understands chemistry and atomic physics. The old idea of lead into gold is out of the question. Instead, they are able to transmute a target up or down one atomic number. The entire target will be changed even if it contains multiple elements. Atomic weight is unchanged. They must be able to handle the target he is going to change. To illustrate:

Target: Water, transmute up. Fail--it falls out of their hands. Target: A beaker of water, transmute up. Hydrogen (protium) unaffected as there's no neutron to change into a proton. Any deuterium becomes He-2 and promptly splits into two hydrogens, or rarely returns to being deuterium. Oxygen-16 becomes F-16 and promptly emits a proton and becomes oxygen-15 and soon N-15. O-17 becomes F-17 which soon returns to O-17. O-18 becomes F-18 which in a little bit returns to O-18. The beaker is basically silicon oxide, Si-28 becomes P-28 which quickly returns to Si-28 or rarely Al or Mg. Si-29 and Si-30 soon return to their original form. The wizard ends up with a very energetic mess in their hands and probably dies. Better pick something else.

Make gold? Transmute mercury down--nope it takes a bit but every isotope produced decays back to being mercury.

Make platinum? Transmute gold down--nope, it decays back to gold. Transmute Iridium up? It's even rarer, no value there.

The only useful transmutation I can find is to transmute Uranium up and the demand there is low. The three isotopes of Neptunium you get all decay fairly soon, two go back to being uranium but Np-238 goes to Pu-238, useful in nuclear batteries. They are all alpha or beta decays, easily shielded against with a thin lead shell that becomes bismuth with decently long half lives. (There may be other elements that can shield it, I stopped looking when I found one that would be safe enough.)

Is there any other useful application of this? The results must be valuable, reasonable to handle and not fry the wizard.

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    $\begingroup$ If all he's doing is transmuting stable materials into unstable ones, then it seems likely he doesn't have the process quite correct. Does he not understand how to suspend the atomic forces or how to use Nescio's Separator? Can you explain the wizard's process a little better, because with all due respect, all the examples seem pretty useless. $\endgroup$
    – elemtilas
    Jul 29, 2021 at 19:42
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    $\begingroup$ Is there a limitation that transmutation can't be applied twice? For example, if he is transmuting 198Hg => 198Au, the latter has a half life of 2.69 days, which may be enough to transmute it into a stable 198Pt. $\endgroup$
    – Alexander
    Jul 29, 2021 at 20:23
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    $\begingroup$ Is this science-based or hard-science? $\endgroup$ Jul 29, 2021 at 21:33
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    $\begingroup$ @Goodies A lot of good SF uses a handwave or two but otherwise plays fair with the laws of physics. That's what I'm picturing here. $\endgroup$ Aug 1, 2021 at 3:13
  • 1
    $\begingroup$ Precisely for that reason !! good science fiction (imho) does not need wizards. Isn't a wizard part of fantasy literature ? not SF literature ? Anyway.. I'll stop making comments now, apparently we differ opinion on SF, and opinion should not play a role here. Success with your topic ! $\endgroup$
    – Goodies
    Aug 2, 2021 at 12:50

8 Answers 8

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This is one of those questions that been bugging me since I first read it, each time I go back, I find more details. It's also given me an excuse to work out how to use the ENSDF data sets with nudel and the NUBASE data set. (And I have a million tabs open and have probably got myself onto some government watch list, but hey-ho.)

It's a long time since I did nuclear physics formally, so I'll need other people to correct any errors.

A few notes:

  • I'll be doing a lot of rounding to order of magnitudes because the numbers don't need to be that accurate.
  • Calculating absorbed doses is hard so I'll be even vaguer there. If someone can do real dose calculations, that'd be nice.
  • I'll be using the uranium to plutonium shielded by lead example from the question for several examples. That's not because this is an unusually bad choice (it's not), I just want to limit the examples I swap between.

Anyway, here are the things I've found.

Nuclear physics is out to kill you

I know it's considered bad form to anthropomorphise fundamental forces, but when it comes to radiation, assume it's in the corner, cackling at you, trying to decide between the quick thrill of instant vaporisation or the slow drawn out agony of radiation poisoning.

It may not seem professional, but you'll live longer. I hope by the end of this discussion you'll agree that I'm not over-reacting.

You're going into unknown territory

Perhaps its no surprise that most of the good quality data comes from isotopes with moderate or long half-lives. It's difficult to get good quality data when your experimental material disappears as you're trying to measure it.

That's not so say there's no data, just that it's lower quality.

The physics of nuclei is very complicated. Even though right at the basics, the underlying quantum mechanics is similar to atomic physics, most approximations fail. For example, nuclei may adopt a non-spherical shape to reduce their energy (see the Nilsson model). Theory often is not a good guide.

You're going to be pushing materials into short-lived isotopes. There may be surprises there.

At least you said a "modern" wizard. When preparing this answer I could look up lots of values (want to know the heat capacity of neptunium? no problem).

How are you balancing charge?

You correctly talk about elemental transformation, rather than nuclear transformation. Transforming just the nucleus would leave you with an imbalance of charge, each mole (at best, a couple of hundred grams) of material transformed would acquire 100 kC of charge, about a thousand times the charge in a lightning bolt, which is going to disintegrate the material.

So, the question is how are you balancing the charge. The natural answer to this is just to do it how beta decay does it which is to create or destroy the appropriate number of electrons.

This suggests a physical mechanism for the magic. If the magic alters the nuclear forces in a region, so that different isotopes were stable then beta decay would do the work of transforming the nuclei. This is the mechanism used in Isaac Asimov's The Gods Themselves, in that case by moving the material to a different universe with different physical laws. However, looking in more detail shows this to be a bad idea.

Balancing with positrons is a bad idea

Nuclei where it would be energetically favourable to decay to lower Z have two choices: electron capture or positron emission. If the difference in binding energy is low, only electron capture is possible. You really want electron capture. If using magic to transform to lower Z emitted positrons, then these would immediately annihilate with electrons in the material causing a burst of gamma rays. Each annihilation will produce two photons for a a total of about 10²⁴ gamma rays per mole of material. Each photon carries about half an MeV, for a total of about 100 kJ per mole of material which I think will be fatal for anyone standing close by.

Balancing with high energy electrons is a bad idea

Electrons emitted by beta decay normally have far too much energy to remain bound to the atom from which they came. This is going to leave ionised material. If every atom in a material ionised simultaneously then what you have now is a plasma. Containment is going to be a problem.

It's not an accident that the electrons aren't bound. Differences in mass excesses between nuclei is usually of the order of MeV and electron binding energies are of the order of eV.

You might think that if you were achieving the the transmutation by altering nuclear forces, you could arrange them so the left over energy was just enough to leave the electron bound. This is unlikely to be practical. If I recall correctly, the beta decay rate goes as the fifth power of the energy difference. So, reducing a energy difference from 1 MeV to eV, will reduce the decay rate by thirty orders of magnitude. That's going to be a long wait.

Molecules will be broken

So, let's assume the magic can take one neutral atom and convert it into another neutral atom with the electron in its lowest energy state. You'll have altered the number of valence electrons available for chemical bonds. If the atom were part of a molecule then the chemical bonds will be broken and the material is likely to disintegrate.

As the chemical bonds reform, you may end up with a sudden chemical reaction happening at every part of the material simultaneously. This is rate not normally seen in nature and could lead to much excitement.

Bulk materials aren't always safe

Even if there are no bonds between different elements, bonds between identical atoms can be problematic. You don't want to end up with a pile of atoms that Suddenly Want To Turn Back Into Elemental Nitrogen.

Maybe transforming one bulk metal into another bulk metal might be the least dangerous.

Or, extend the magic to place the electrons in a suitable position for the new material.

The physical change in the material is a problem

Even a bulk material may have a different preferred configuration from its starting material.

A dramatic case is transforming from an atom that wants to be a solid at room temperature to one that wants to be a gas (say, potassium to argon). This is going to cause an explosion for any non-trivial quantity.

However, even solid to solid transformations can be a problem. In the original question there's a suggestion of putting a shield of lead around the material on the assumption that when it transforms to bismuth it will still be a good shield. Even if that's true, bismuth is about 10% less dense than lead so the material will suddenly be under a lot of stress as the atoms would prefer to be further apart. That's assuming it doesn't want to change its crystal structure. There would be a serious question as to whether the material would retain enough structural integrity to act as a good quality shield.

Chemical impurities are going to kill you

As written, the magic transforms all atoms in the affected region. Getting high quality chemical purity is going to be a problem.

Let's suppose you left one microgram of carbon-12 somewhere in the material being transformed: perhaps a fingerprint on the outside, or some cleaning solvent trapped in the surface irregularities. Transforming carbon-12 up or down to boron-12 or nitrogen-12 gives a substance with a half-life of tens of milliseconds.

This is going to release about 10¹⁷ beta particles all at once (by the standard of human reaction times). This is equivalent to standing next to a 100 TBq source for about ten minutes.

In the case of transforming up to nitrogen-12, the beta particles are positrons so you get a similar number of annihilation gamma rays as well.

Transforming hydrogen in the material down will give a pulse of (presumably thermal) neutrons at a similar sort of level.

Isotopic impurities are going to kill you

Even if you can chemically purify your material, you still have to worry about isotopic impurities.

Taking the lead to bismuth shielding transformation from the question. The intention is to use lead-208 to give bismuth-208 with a half-life of 3×10⁵ years. However, without isotopically purifying the lead, only half of it will be lead-208. A quarter will be lead-206 (I'll ignore the remaining quarter of the lead). That transforms to bismuth-206 which has a half-life of six days.

Suppose the shielding used only 1 g lead, so the result is 0.5 g of bismuth-208 and 0.25 g of a gram of bismuth-206. The bismuth-208 has a radioactivity of about 100 MBq which isn't too bad. However, the bismuth-206 is about 1 PBq which is a problem.

If you are transforming chemically pure hydrogen then transforming it up is going to turn the deuterium into helium-2 which is unstable and will immediately decay into two protons.

Although it's possible to enrich material, it's an expensive process. Getting it isotopically pure is difficult. If we could cheaply purify bulk materials then we'd use it to reduce soft-errors in computer chips and we wouldn't need to recover lead from shipwrecks.

Even a thousand-fold reduction of the bismuth, in example above, merely reduces the radioactivity to 1 TBq.

There are a small number of elements where there's only one naturally occurring isotope. For these, you could use chemical techniques to get good isotopic purity. These are: ⁹Be, ¹⁹F, ²³Na, ²⁷Al, ³¹P, ⁴⁵Sc, ⁵⁵Mn, ⁵⁹Co, ⁷⁵As, ⁸⁹Y, ⁹³Nb, ¹⁰³Rh, ¹²⁷I, ¹³³Cs, ¹⁴¹Pr, ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁹Tm, ¹⁹⁷Au, and ²⁰⁹Bi.

Strictly, Protactinium has only one naturally occurring isotope (²³¹Pa) but seeing that has a short half-life (30,000 years) it's present only because of decay of other particles and any sample is likely to become contaminated with its decay products so we can drop that.

Similarly, one source I used would put ²³²Th on this list as being the only naturally occurring isotope, but another source reports a 0.02% mixture of ²³⁰Th, so I've omitted it.

It turns out none of these are interesting. Most don't have long-lived isotopes within two protons of them. The full list is (with half-lives, "a" is years):

A Z−2 Z−1 Natural Z+1 Z+2
9 ⁹He (very short) ⁹Li (178.3 ms) ⁹Be (stable) ⁹B (0.54 keV) ⁹C (126.5 ms)
19 ¹⁹N (271 ms) ¹⁹O (26.88 s) ¹⁹F (stable) ¹⁹Ne (17.22 s) ¹⁹Na (< 40 keV)
23 ²³F (2.23 s) ²³Ne (37.25 s) ²³Na (stable) ²³Mg (11.3046 s) ²³Al (446 ms)
27 ²⁷Na (301 ms) ²⁷Mg (9.458 min) ²⁷Al (stable) ²⁷Si (4.15 s) ²⁷P (260 ms)
31 ³¹Al (644 ms) ³¹Si (157.36 min) ³¹P (stable) ³¹S (2.5534 s) ³¹Cl (190 ms)
45 ⁴⁵K (17.81 min) ⁴⁵Ca (162.61 d) ⁴⁵Sc (stable) ⁴⁵Ti (184.8 min) ⁴⁵V (547 ms)
55 ⁵⁵V (6.54 s) ⁵⁵Cr (3.497 min) ⁵⁵Mn (stable) ⁵⁵Fe (2.744 a) ⁵⁵Co (17.53 h)
59 ⁵⁹Mn (4.59 s) ⁵⁹Fe (44.490 d) ⁵⁹Co (stable) ⁵⁹Ni (7.6×10⁴ a) ⁵⁹Cu (81.5 s)
75 ⁷⁵Ga (126 s) ⁷⁵Ge (82.78 min) ⁷⁵As (stable) ⁷⁵Se (119.78 d) ⁷⁵Br (96.7 min)
89 ⁸⁹Rb (15.32 min) ⁸⁹Sr (50.563 d) ⁸⁹Y (stable) ⁸⁹Zr (78.41 h) ⁸⁹Nb (2.03 h)
93 ⁹³Y (10.18 h) ⁹³Zr (1.61×10⁶ a) ⁹³Nb (stable) ⁹³Mo (4.0×10³ a) ⁹³Tc (2.75 h)
103 ¹⁰³Tc (54.2 s) ¹⁰³Ru (39.247 d) ¹⁰³Rh (stable) ¹⁰³Pd (16.991 d) ¹⁰³Ag (65.7 min)
127 ¹²⁷Sb (3.85 d) ¹²⁷Te (9.35 h) ¹²⁷I (stable) ¹²⁷Xe (36.346 d) ¹²⁷Cs (6.25 h)
133 ¹³³I (20.83 h) ¹³³Xe (5.2475 d) ¹³³Cs (stable) ¹³³Ba (10.551 a) ¹³³La (3.912 h)
141 ¹⁴¹La (3.92 h) ¹⁴¹Ce (32.511 d) ¹⁴¹Pr (stable) ¹⁴¹Nd (2.49 h) ¹⁴¹Pm (20.90 min)
159 ¹⁵⁹Eu (18.1 min) ¹⁵⁹Gd (18.479 h) ¹⁵⁹Tb (stable) ¹⁵⁹Dy (144.4 d) ¹⁵⁹Ho (33.05 min)
165 ¹⁶⁵Tb (2.11 min) ¹⁶⁵Dy (2.332 h) ¹⁶⁵Ho (stable) ¹⁶⁵Er (10.36 h) ¹⁶⁵Tm (30.06 h)
169 ¹⁶⁹Ho (4.72 min) ¹⁶⁹Er (9.392 d) ¹⁶⁹Tm (stable) ¹⁶⁹Yb (32.018 d) ¹⁶⁹Lu (34.06 h)
197 ¹⁹⁷Ir (5.8 min) ¹⁹⁷Pt (19.8915 h) ¹⁹⁷Au (stable) ¹⁹⁷Hg (64.14 h) ¹⁹⁷Tl (2.84 h)
209 ²⁰⁹Tl (2.162 min) ²⁰⁹Pb (3.234 h) ²⁰⁹Bi (2.01×10¹⁹ a) ²⁰⁹Po (124 a) ²⁰⁹At (5.42 h)

For half-lives of over a million years (see below), there's Niobium-93 to Zirconium-93. For half-lives over a thousand years there's also Cobalt-59 to Nickel-59 and Niobium-93 to Molybdenum-93 and

Unshielded nuclei are either stable or going to kill you

People have been a bit blasé about letting materials beta decay after the transformation assuming that radiation isn't a problem. However, people are normally used to dealing with tiny quantities of radioactive materials with short half-lives where, in this context, "short" can mean years. As a rule of thumb, it's best to avoid interaction with gram (or kilogram or tonne) quantities of materials with half-lives below a million years. For milli- or microgram quantities you might be safe with shorter half-lives (thousands of years and years respectively).

You can see from the example above, that bismuth-208, with a half-life just below the million year mark I gave, is just about handleable in at the gram level. Radioactivity rates are inversely proportional to half-life. So, a material with a half-life of one year has a million times the radiation flux of a material with a half-life of a million years.

I'm not kidding, even the heating will kill you

In the same example, the goal is to transform uranium-238 to plutonium-238 via neptunium-238 to make a nuclear battery. Let's assume everything is isotopically pure

A radioactive heater unit might contain 34 g of plutonium-238. I think that's going to produce about 20 W of heat which is containable in 34 g of bulk material (it's about 5 °C/s of heating). The neptunium-238 has a half-life about ten thousand times shorter. After correcting for the different decay energies, the 34 g of neptunium produces about 100 kW and heats up at 20,000 °C/s (assuming the radiation is absorbed within the bulk of the material) meaning it vaporises about 200 ms after it's formed. A boiling cloud of neptunium (emitting about 400 PBq of radiation) is going to shatter a thin shield, melt its way through a thick shield and ruin your day.

Two nucleons are better than one

With a half-life threshold set at a million years, there are so few single nucleon transformations that give a suitably long-lived product, that it's possible to list them all:

  • ¹⁰B → ¹⁰Be (1.51×10⁶ a)
  • ⁴⁰Ar → ⁴⁰K (1.248×10⁹ a)
  • ⁴⁰K → ⁴⁰Ar (stable)
  • ⁴⁰K → ⁴⁰Ca (stable)
  • ⁵⁰Ti → ⁵⁰V (2.65×10¹⁷ a)
  • ⁵⁰V → ⁵⁰Ti (stable)
  • ⁵⁰V → ⁵⁰Cr (> 1.3×10¹⁸ a)
  • ⁵⁰Cr → ⁵⁰V (2.65×10¹⁷ a)
  • ⁵³Cr → ⁵³Mn (3.7×10⁶ a)
  • ⁸⁷Rb → ⁸⁷Sr (stable)
  • ⁸⁷Sr → ⁸⁷Rb (4.97×10¹⁰ a)
  • ⁹²Zr → ⁹²Nb (3.47×10⁷ a)
  • ⁹²Mo → ⁹²Nb (3.47×10⁷ a)
  • ⁹³Nb → ⁹³Zr (1.61×10⁶ a)
  • ⁹⁷Mo → ⁹⁷Tc (4.21×10⁶ a)
  • ⁹⁸Mo → ⁹⁸Tc (4.2×10⁶ a)
  • ⁹⁸Ru → ⁹⁸Tc (4.2×10⁶ a)
  • ¹⁰⁷Ag → ¹⁰⁷Pd (6.5×10⁶ a)
  • ¹¹³Cd → ¹¹³In (stable)
  • ¹¹³In → ¹¹³Cd (8.04×10¹⁵ a)
  • ¹¹⁵In → ¹¹⁵Sn (stable)
  • ¹¹⁵Sn → ¹¹⁵In (4.41×10¹⁴ a)
  • ¹²³Sb → ¹²³Te (> 9.2×10¹⁶ a)
  • ¹²³Te → ¹²³Sb (stable)
  • ¹²⁹Xe → ¹²⁹I (1.57×10⁷ a)
  • ¹³⁵Ba → ¹³⁵Cs (2.3×10⁶ a)
  • ¹³⁸Ba → ¹³⁸La (1.03×10¹¹ a)
  • ¹³⁸La → ¹³⁸Ba (stable)
  • ¹³⁸La → ¹³⁸Ce (> 4.4×10¹⁶ a)
  • ¹³⁸Ce → ¹³⁸La (1.03×10¹¹ a)
  • ¹⁷⁶Yb → ¹⁷⁶Lu (3.76×10¹⁰ a)
  • ¹⁷⁶Lu → ¹⁷⁶Yb (stable)
  • ¹⁷⁶Lu → ¹⁷⁶Hf (stable)
  • ¹⁷⁶Hf → ¹⁷⁶Lu (3.76×10¹⁰ a)
  • ¹⁸⁰Ta → ¹⁸⁰Hf (stable)
  • ¹⁸⁰Ta → ¹⁸⁰W (1.8×10¹⁸ a)
  • ¹⁸⁷Re → ¹⁸⁷Os (stable)
  • ¹⁸⁷Os → ¹⁸⁷Re (4.33×10¹⁰ a)
  • ²⁰⁵Tl → ²⁰⁵Pb (1.70×10⁷ a)

That's a total of 39 possibilities. If you're prepared to drop the half-life safety threshold to one thousand years, you can add another 15.

It's not an accident that there are no good single nucleon transformations.

You'll notice that, in all the cases I listed, one of the two nuclei is radioactive, albeit with usefully long half-lives. This is consequence of the Mattauch isobar rule.

Beta decay will exploit quite small differences in mass excesses (by the scale of the total binding energy of the nucleus). You can imagine that nominally, a plot of mass excess versus protons for constant mass, has a U shape and isotopes beta decay down the sides to the middle. If this were the case there'd be only one stable isotope per mass.

There are a number of effects that prevent the sides of that plot being smooth. The most important is that nucleons like to pair up. If you're familiar with filling electron shells in atoms you'll be aware that electrons preferentially fill each shell with one electron before going back and filling in its pair. For nuclei it's different. It's energetically favourable to pair the nucleons first. So, nuclei with even number of protons and neutrons are more tightly bound than those with odd numbers.

This superimposes an even-odd zig-zag on the U shape. So, at the bottom of some Us there can be two local minima separated by two protons. The Z between these two is typically unstable, preferring to beta decay to either, or both, of the two adjacent nuclei.

So, if you can move by two nucleons, you don't create unpaired nucleons and there are many more possibilities: 136 with a million year half-life cutoff, and only an additional two with a thousand year cutoff (see also Isobar stability).

A couple of interesting ones are:

  • ¹⁹⁶Hg → ¹⁹⁶Pt (stable)
  • ¹⁹⁸Hg → ¹⁹⁸Pt (stable)

Mercury-196 is only about 0.15% of natural mercury but mercury-198 is about 10%. Needless to say, these will need to be isotopically pure. The other isotopes of mercury, 199, 200, 201, 202 and 204 do not have stable platinum isobars. The most stable has a half-life of 12.5 hours, the least stable is unbound.

Two nucleons once is better than one nucleon twice

It's already been suggested that the wizard can perform the magic twice to move by more than one proton. The problem is that the element between two stable isobars often has a very short half-life. Taking the mercury to platinum transformations I just listed, in both cases, the intermediate gold nuclide has half life of a few days and by now you know where this is going. These will produce petabecquerels of radiation per gram, and about a kilowatt of power per gram.

You need to change the rules

If you don't change the rules of your wizard's magic there's no good ending. The wizard has only useless transformations and the transformation of trace contaminants will be fatal.

As already noted, changing the wizards magic to move two nucleons is a big help. The next is to change the selectivity. If the wizard can target specific nuclides then the contamination problem disappears.

Maybe you can work the selectivity into the story as the wizard's special ability. It's easy to assume that the problem with magic is power, but maybe it's control. Perhaps, by analogy, when casting fireball the problem is not getting the fire: just open a portal to the elemental plane of fire. Perhaps 99% of the fireball spell is getting the fire to its target instead of boiling the wizard's brain.

So, if your wizard can control their magic, tune it to the right nuclides, let the transformation go slowly to give the material time to relax and cool from atomic shifts, then maybe they can survive to do something useful.

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  • $\begingroup$ Wow! I didn't realize how hot the intermediates would be. You seem to have found better shields than I did (I stopped when I saw the lead->bismuth, I didn't realize it wouldn't work.) The thermal issues are a complete showstopper, though--I was thinking the wizard could just immediately drop the material into a cooling tank, I didn't realize it was so hot that wasn't an option. $\endgroup$ Aug 10, 2021 at 15:32
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Look at the full chemical reactions, not just the atomic decay

OPPS! F-16 HAS A 10^-20 SECOND HALF LIFE; SO, MY ORIGINAL ANSWER DOES NOT WORK AS WRITTEN ... THANKS COMMENTS.

Lets go back to your water example. Good old H2O has O-16 with its two covalent bonds but turns into F-16 with 1 covalent bond. During this short period of having F-16 your H20 will momentarily become hydrogen fluoride and hydrogen gas.

2(H2O) -> 2(HF) + 1(H2)

If you perform this transmutation at a temperature under 67°F (~20°C) then the hydrogen fluoride will pool as a liquid and the hydrogen will fly away as a gas. The hydrogen gas can now be collected if you so choose, but is not really the valuable half of this equation. It's only worth about \$0.40-0.70 per gallon of water.
However, when the Florine decomposes back into Oxygen, you will now have a 1:1 ratio of Oxygen and Hydrogen leaving you with a very pure (and possibly dangerous) hydrogen peroxide.

2(HF) -> 1(H2O2)

As it turns out hydrogen peroxide is worth a good bit more than water. In the United States the average cost of tap water is \$0.004 per gallon, and hydrogen peroxide is typically sold at 3% H2O2 and 97% H2O for \$13.00-14.00 per gallon. So, if you take a 30 gallon drum of tap water, and just transmute about 1 gallon at the core of the drum, the water will appear to boil as the hydrogen gas escapes, turning the liquid into a weak hydrofluoric acid, and then decaying into a hydrogen peroxide solution. Out of this reaction you will get about \$400 worth of 3% hydrogen peroxide using only \$0.12 worth of water.

... That said, chemical reactions are still the way you profit from this discovery. One such case could be a possibly cheaper alternative to the Hall–Héroult process in the refining of aluminum.

By phasing down Aluminum Oxide, you get Mg-27 (2 bonds) for about 10 minutes per half life and N-16(3 bonds) for 7 seconds per half life. So the first reaction that would happen is that a lot of that Nitrogen will be forced out of the compound. Leaving you with Magnesium Nitride and Nitrogen gas. You use this opportunity to physically separate the compounds (perhaps with a vacuum chamber?)

6(Al2O3) -> 4(Mg3N2) + 5(N2)

A over the next few seconds most of the nitrogen will decompose into Oxygen leaving you with mixture of Magnesium Oxide and pure Magnesium in the vacuum chamber.

1(Mg3N2) -> 2(MgO) + 1(Mg)

Then several minutes later your Magnesium will go back to Aluminum yielding a partially refined aluminum mixture.

6(MgO) + 3(Mg) -> 2(Al2O3) + 5(Al)

Repeat the process a few times, and soon you will have a mostly pure aluminum dust ready to be smelted. A similar process could work on just about any oxide based ore (hematite, titanium oxide, etc.), but Aluminum is notoriously one of the harder ones to refine so it would probably yield the most profit.

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    $\begingroup$ +1 Basically, you have invented a completely new family of catalyzers. $\endgroup$
    – Rekesoft
    Jul 30, 2021 at 7:19
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    $\begingroup$ It's like the Pratchett alchemists, who could only turn gold into less gold. All you need is enough copper wire to build a small town wound around a football stadium and enough electricity to power aforesaid town, and you can increase the value of five litres of water to $400. Alternately you can take photos of the sparkles and write your doctoral thesis. $\endgroup$
    – Peter Wone
    Jul 30, 2021 at 7:32
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    $\begingroup$ Decay of F16 is as fast as 10^-20 seconds (en.wikipedia.org/wiki/Isotopes_of_fluorine). You aren't getting any chemistry done in that amount of time. $\endgroup$ Jul 30, 2021 at 12:50
  • $\begingroup$ @ZizyArcher Thanks, see revised answer. $\endgroup$
    – Nosajimiki
    Jul 30, 2021 at 15:20
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    $\begingroup$ @LorenPechtel I think you need to better define "reasonable to handle" then. Does he need to handle it with his bare hands? Be within a certain proximity? need to be able to see it? Most of what we "transmute" using modern science involves thick furnaces and/or radiation shielding. $\endgroup$
    – Nosajimiki
    Jul 30, 2021 at 21:59
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Atomic waste disposal?

There's a problem with certain fairly long-lived isotopes which have to be stored for many years or centuries before natural decay renders them harmless. Using this trick on them might well render them much less stable. If the subsequent decay is an alpha-decay, you have jogged them off one decay chain and onto another, and the resulting waste may be less of a long-term problem (though of course it becomes much hotter in the short-term).

Nuclear power generation?

This last factor might also mean that you have opened up a new form of magically catalyzed nuclear power. Start with a "useless" heavy element such as U238 or Thorium 232, magically move it out of its long-term almost-stable state in a reactor core, and generate lots of electricity.

Bombs?

Take care. Transmuting into something with a very short half-life could result in a catastrophic release of energy in the next seconds or microseconds. If you could accomplish this trick at a distance, you have a new weapon system. If not, you have a self-preservation issue.

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  • $\begingroup$ Hey, I like the waste disposal one. It's certainly not useful for bombs--everyone's ignoring the condition that the wizard has to be able to handle both the original and the result. $\endgroup$ Jul 30, 2021 at 20:16
  • $\begingroup$ This takes the medal. There are lots of things with short enough half-lives to be of concern, but long enough half-lives that they just promptly self-decay like Iodine 131 does. They could be safely handled long enough to transmute them. Also making PU238 for RTGs. $\endgroup$ Jul 31, 2021 at 2:16
  • $\begingroup$ @Harper-ReinstateMonica I already saw the U238 -> Pu238 path. That's the only high-value one I could find and the demand for RTGs is limited. The space programs will pay a bunch for some but the market very quickly will saturate. $\endgroup$ Jul 31, 2021 at 20:28
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If they can transmute the Sun's helium back into useful hydrogen fuel, they can add several billion years to the Earth's window of supporting life. Not a one-day task, obviously, since we like the sun the way it is. That seems useful, though perhaps not particularly profitable without a good Kickstarter video.

They can also convert CO2 into Carbon and Oxygen (via N-12 and F-16). Some of the carbon would combine with other carbon, precipitating carbon dust out of the reaction chamber. Quite a few companies (and governments) would pay them to offset their emissions, and others would pay them for the precipitated carbon dust.

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    $\begingroup$ If all Helium-4 inside the Sun was suddenly converted to Hydrogen-4, the Sun would likely go supernova. $\endgroup$
    – Alexander
    Jul 29, 2021 at 20:31
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    $\begingroup$ Yes, well, let's not do the entire Sun on on the same day, then. A bit at a time to prevent indigestion. Edited to address. $\endgroup$
    – user535733
    Jul 29, 2021 at 20:33
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    $\begingroup$ +1 for equating the effort needed to add billions of years to the Sun's life to a kickstarter campaign. I might laugh for a week. Well done! $\endgroup$ Jul 30, 2021 at 3:24
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    $\begingroup$ "Must be able to handle the item to be transmuted" -- I see a problem trying to "handle" the core of a star... $\endgroup$
    – Zeiss Ikon
    Jul 30, 2021 at 11:02
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    $\begingroup$ @Chris Charabaruk - any known type of supernova - no. Violent star explosion, which an outside observer can classify as supernova - yes. $\endgroup$
    – Alexander
    Jul 30, 2021 at 21:36
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Looks to me as if transmuting iron into cobalt would produce isotopes with long enough half life and useful enough properties to be worth considering.

One isotope of iron, atomic weight 57, would give a cobalt isotope with a half life of 271+ days, decaying back to iron by electron capture. However, you'd also get small amounts of cobalt 60, very useful for radiation treatments of certain cancers and irradiation preservation of food (gamma emitter). The other most common isotopes of iron, 56 and 58, produce beta emitters with a half life of 70 and 77 days, respectively, which decay to manganese isotopes which then decay (over a period of days) to chromium.

The key here is that you'd have months in which to process the cobalt to enrich the cobalt-60, potentially cutting the cost of production of this isotope (normally created by neutron bombardment in a nuclear reactor) and therefore reducing the cost of food irradiation units and other gamma ray sources.

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  • $\begingroup$ Actually, the most common isotope of iron is Fe-56, at nearly 92%. $\endgroup$
    – Glen O
    Jul 30, 2021 at 5:48
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This wizard might be able to desalinate water, which would help millions of people facing water shortages. This would work best if the wizard can teach others to do the same.

My thought process is that the wizard gets barrels of water, or whatever they can handle in one shot, and transmutes the NaCl to Neon and Sulphur. The neon, being a Nobel gas, would break the connection to sulphur and bubble out of the water. The sulphur should start to settle to the bottom and some can be removed that way before it turns back into chlorine by simply sucking out the bottom portion of the water or closing it off from the majority of the container. Collecting the neon for use as sodium for when it turns back might be useful.

When the sulphur turns back into chlorine, it essentially disinfects the remaining water. Much of it would bubble out of the water, too. Capturing it might be useful.

I was thinking the next step is to transmute the chlorine into argon. My idea was this should bubble out of enough so that when it turns back into chlorine, but that's still seems to be about 15 times too much chlorine to be safe drinking water, so the next steps are to keep turning the chlorine into sulphur so it continues to settle out, since it's insoluble with water.

The water concentrated with sulphur that was removed is used as chlorine bleach.

The thing that would make this most useful is teaching this skill to others. One wizard being able to do this is nice, but probably has a significant cap as to how much desalinated water can be produced in a given time. Teach this to thousands or millions, and you have a much more useful process.

Granted, there are likely other things that need to be removed from seawater, so transmute them in ways to get them out as well. This might require transmuting something else to cause a chemical reaction to get the contaminates to either settle or bubble out.

I'm not familiar enough with the whole process of turning seawater into drinkable water to know what else is needed, but this seems like a good start. Even if the process is too dangerous to be done by "the average Joe" at home or the beach, it can still be done in controlled processing plants by trained "engineers". Having thousands of these plants around the world would likely be easier and cheaper to build, maintain, staff, and be less environmentally damaging than current desalination plants.

With the waste products from this process being (mostly) chlorine and sodium, we can use them as is or recombine them to produce the salt we already get from seawater.

The wizard might not get rich off the clean water, bleach, etc., but the process itself could be worth millions in tuition fees. Then again, clean water, bleach, and salt are billion dollar industries themselves.

Research:

Safe drinking water has up to 0.0151416 g/gal (4 ppm) of chlorine in it.
https://www.cdc.gov/healthywater/drinking/public/water_disinfection.html

However, swimming pools have a minimum of 1 ppm and spas should have 3 ppm chlorine in them, so 4 ppm is probably not going to be very palatable.
https://www.cdc.gov/healthywater/swimming/residential/disinfection-testing.html

Solubility in water

Neon: 10.5 cu cm/kg (with a density of 0.899994 kg/cu m) = 3.24461703e-4 g/gal
https://pubchem.ncbi.nlm.nih.gov/compound/Neon#section=Melting-Point

Argon: 62 mg/L = 0.234696 g/gal
https://www.lenntech.com/periodic/water/argon/argon-and-water.htm

Salt: 360 g/1000 g = 1363 g/gal
https://en.wikipedia.org/wiki/Sodium_chloride

Chlorine: 6.93 lbs/100 gal = 31.4 g/gal
https://www.chlorineinstitute.org/stewardship/chlorine/chemical-properties/

Sulphur: Sulfur is insoluble in water
https://en.wikipedia.org/wiki/Sulfur

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  • $\begingroup$ No targeting like this. The whole target is transmuted (except for the hydrogen which has no way to be transmuted up as there are not enough particles in the nucleus.) $\endgroup$ Jul 31, 2021 at 20:23
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This one depends on whether or not the result has to actually have protons and electrons, but maybe you could use it to create neutrons for nuclear experiments in large quantities.

Take a canister of hydrogen and transmute it down. The proton and electron in the hydrogen combine to create a neutron. Deuterium would create two neutrons, and tritium, three.

Of course, the results would be highly radioactive, given free neutrons have a half-life of about ten minutes and undergo beta decay to protons and electrons, but maybe your wizard can come up with a way to shield themselves.

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As a side note, it's important to consider the electrons as well. Going up, transforming a spoonful of water will change roughly 10^23 neutrons into protons. That's around 10^4 coulombs, which is a lot. Electrons from the moon will feel an acceleration of ~10^8 m/s^2. This will cause massive electrical storms, and probably sterilize the planet of all life. A similar analysis applies to going down.

Thus, the only reasonable alternatives are n -> p+e (beta radiation) or p+e -> n (electron capture).

The other answers provide good, practical uses, but there's also a serious security threat that needs to be addressed: suicide bombers. Since F16 has a very short half life, changing O16->F16 will result in a massive release in energy. If ISIS can sneak an alchemist into the USA, they can easily wipe the entire country out by transmuting a large pond, or if the effects are more limited, they can still wipe out a major city by transmuting a barrel of water.

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  • $\begingroup$ I'm not getting the maths at all. 10^23 neutrons into protons would yeald 10^23 electrons - wouldn't that be a charge of approximatley 1.7 coulombs? Also, I might have missed something, but what moon? Anyhow, welcome to worldbuilding, take our wonderful tour and read-up in the help center about how we work (when you've the time to read it, it's not brief), enjoy the site. $\endgroup$ Aug 2, 2021 at 1:41
  • $\begingroup$ I figured n -> p+e and p+e -> n reactions. Anything else would be far too energetic to be around and thus make it useless other than to suicide bombers. I'm not seeing your blast energies, though. $\endgroup$ Aug 2, 2021 at 3:57

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