Is it possible to obtain gold through nuclear decay? Is there a series of transmutations through nuclear decay that will result in the stable gold isotope ${}^{197}\mathrm{Au}$ ? How long will the process take? 
 A: The following wikipedia link has a table of all the known isotopes of all the known elements. Gold has Z=79. According to the table, there's only one stable isotope of gold, $\;^{197}Au$ :
http://en.wikipedia.org/wiki/Table_of_nuclides_%28complete%29
From this you can figure out which isotopes decay into gold by considering the three possible decays (ignoring fission) beta decay, inverse beta decay, and alpha decay.
Beta decay means a neutron decays into a proton, an electron and an anti neutrino. The electron and anti neutrino go away. So the result is that the number of neutrons ("n" in the above table) decreases by one while the number of protons ("Z" in the above table) increases by one. The result is that you move in the table one square diagonally towards the top right.
Inverse beta decay is the opposite of beta decay (more or less). The result is that you move one square diagonally towards the bottom left.
Alpha decay means the loss of a helium nucleus of 2 protons and 2 neutrons. So you move two squares diagonally to the top left.
So if you want to look for chains that end with gold, do the following. Look at the isotopes 2 squares down and to the right (for alpha decay) or diagonally one square up right or down left (for beta decays). Now take a look at that isotope to see if it decays in the manner you've assumed. For example, $\;^{195}Hg$ is in a position to beta decay to gold.
To find out whether the isotope decays the way you've assumed, go to this website:
http://ie.lbl.gov/toi/perchart.htm
and click on the element, then the isotope. Clicking on Hg and then the isotope 195 shows that it does indeed decay to gold.
Note that this isotope can decay to gold in something like 46 ways. The different ways involve various excited nuclear states for either the mercury or the gold or both. Such excited states may also decay by emission of a photon (gamma ray).
A: Last time I did the sum, 201Hg to 197Au plus 4He did not need external energy:
200.970277 - (196.9665516 + 4.0026032) = 4.0037254 - 4.0026032 = 0.0011222. 
Caveats: 


*

*I did not check the error term of atomic weigths, and

*The first decay, alpha to 197Pt, should be awesomely slow. In fact

*201Hg is considered stable in all the listings.


But the point is that the external energy would be recovered in this case.
A: the alchemists have dreamed about the production of gold (Z=82) from some cheap material and lead (Z=79) was their favorite choice. They were just using a wrong science - namely primitive chemistry instead of nuclear physics. But otherwise their choice of lead was OK. And indeed, lead became the element that was transmuted into gold for the first time sometime in 1980 (and maybe even in 1972). See
http://chemistry.about.com/cs/generalchemistry/a/aa050601a.htm
One has to remove three protons which costs a lot of energy. Needless to say, the transmutation remains economically unacceptable. That's true for other strategies, too.
Best wishes
Lubos
A: Natural gold exists, so the answer to the first part of your question is unambiguously "Yes". 'Cause all those heavy elements get made by transmutation in supernovae.
I can't answer the time scale thing because I haven't a table of the isotopes in front of me right now.

Checking with http://ie.lbl.gov/education/isotopes.htm I find that $^{197}$Pt has a beta decay branching fraction of about 3% and a halflife of about 95 minutes, and $^{197}$Ir decays by beta with 5 minute halflife and $^{197}$Os decays by beta with a 64 hour halflife...
Anyway, you can chase this as far as you care to.
A: I guess you are really looking for this wikipedia page : http://en.wikipedia.org/wiki/Synthesis_of_noble_metals#Gold .
In short, there are gold synthesis technique, but they apparently all need some external energy (either $\gamma$-ray or neutron capture) and are not restricted to nuclear decay. One of them has for intermediate step the nuclear decay${}^{197}Hg\rightarrow{}^{197}Au+e^+$ with a 2 days half life. The unstable ${}^{197}Hg$ is obtained from a stable $Hg$-isotope by $\gamma$-ray irradiation (${}^{198}Hg+\gamma\rightarrow {}^{197}Hg +n$.)
A: Maybe not. Hg to Pt via a modified fusor where the 201Hg feedstock is obtained by enrichment might just have worked.
There is a hypothesis that if "Die Glocke" existed it could have in fact been a primitive attempt at just that, using intense magnetic fields from LaBaCuO to enrich 201Hg at high speeds in a cold plasma.
The next step would have been to pump down the fusor with a deuterium gas fill and cryogenically cooled 201Hg in the centre, adjusting for the highest possible neutron count. Possible, barely assuming step 1 had worked.
Intriguingly there is anecdotal evidence that LaBaCuO might have been obtained from a German scientist who went to the US as part of "Project Paperclip" and later used for the XB-182 Aurora in the 1960s as part of the atmospheric oxygen harvesting system using cryogenic hydrogen as both fuel and coolant.
A: I made some gold many years ago when we wanted to take measurement with the 77keV gamma. After a bit of literature survey and a botched trial with natural platinum. the preferred method was to get your isotopically enriched 75 mg if I remember, pt196 (from a calutron) add neutrons from a borrowed reactor, leave for a few days and then bring it home. useful life of source was almost a week. then start again with the same source as hardly any of the Pt was transmuted. 
