Re: How many radioactive elements are made only in the labratory?

For several reasons, the answer to this one is a bit more complicated than just saying a number.

(1) There are some radioactive elements that exist (in some cases) or might exist (in others) in 
absolutely minute quantities naturally.

(2) Some of the newer artificial elements -- the very heaviest ones -- are still controversial. They 
have only been prepared in quantities of a few atoms. They last much less than a second. They 
have not been well characterized. In some cases scientists are still arguing about whether they 
really have been made or not.

(3) What do you mean by "in the laboratory"? Some of the large facilities where the super-heavy 
elements are made are rather different from what you would normally think of as a "laboratory". 
Some of the artificial elements are made not only "in the laboratory", but also in nuclear explosions 
or nuclear reactors.

So I will try to deal with your question by running through the elements. With two exceptions, the 
elements from 1(H) to 83(Bi) have stable isotopes, and all are found in nature. The two exceptions 
are 43(Tc) and 61(Pm).

The Earth is about 4.5 billion years old, and the explosion that created the material of the Earth 
somewhere between that age and about double it. So radioactive isotopes with half lives from 
hundreds of millions of years upward might be found in nature, while those with half-lives of a 
mere few million years would all be well gone by now, unless they were being replenished by 
secondary processes.

As well as the elements with stable isotopes, there are two others, 90(Th) and 92(U), with isotopes 
having half-lives of billions of years. These two elements can also be found abundantly in nature.
Both U and Th eventually decay to lead. But they do so in a number of steps via intermediate 
products. Because of this process (known as a "decay series") several unstable elements with 
relatively short lifetimes are found in minute quantities in the ores of U and Th (or in other places 
after escaping from ores of U and Th). These elements are 84(Po), 86(Rn), 88(Ra), 89(Ac), and 
91(Pa). 

That leaves:
(1) elements 43(Tc), 93(Np), and 94(Pu), all of which have isotopes with half-lives in the 100,000 
year plus bracket, and all of which are formed in nuclear reactors or nuclear explosions.

(2) elements 61(Pm) 85(At) 87(Fr), which have no isotopes with long half-lives (25 years for Pm, a 
few minutes for the others).

(3) elements 95(Am) to 98(Cf), which have been artificially produced in reasonable quantities, and 
which have isotopes with long half-lives (over a thousand to millions of years). An americium 
isotope, for example, is often used in smoke detectors.

(4) elements 99-114 and 116. The lifetimes, difficulty of making them, and quantities in which 
they have been made generally get more problematic as you go heavier. How well they have been 
characterized also tends to go down as you get heavier. They have to be made in special particle 
accelerators.

(5) claims for a few heavier elements, on which the jury is still out.

My inclination would be to count only groups 2 & 4, arriving at a figure of 20 elements made "only 
in the laboratory".

You can get much better information than I can provide with a web search on "artificial elements" 
or "synthetic elements".