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What element can destroy the world?

Hydrogen. You can destroy the world with less hydrogen than with any other element, because it's available in smaller quantities than any other element. Of course, it's not easy to destroy the Earth with a single atom of hydrogen.

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$egingroup$

Sulfur

But use it to freeze the earth, not for burning. You only need on the order of $10^{11}$ kg. And all the science is available today. I'm cross-posting this answer from How much Sulfur Dioxide is needed to freeze life on earth?, which was inspired by this question.

What is the extinction mechanism?

I’m going to guess that changing the average temperature from 16 degrees Celcius to -20 degrees will cause enough havok to create mass extinctions. The average temperature during the last ice age was about 10 degrees. If the temperature near the equator ranges from 10-30 above the average, -20 globally would get the temperature there dipping below freezing regularly. This is inspired by Intellectual Venture's hose-to-the-sky cooling scheme for combating global warming, described in Levitt and Dubner’s SuperFreakonomics, where all my citations are coming from. Intellectual Venture’s plan to completely reverse global warming requires 5 base stations, placed strategically across the globe, each with 3 hoses (p. 196) spraying liquified sulfur dioxide into the stratosphere, 7 miles up (p. 189). Each hose sprays at 34 gal/min (p. 192), or 190 kg/min, so 2800 kg/min for all 15 hoses. Since they said this will “effectively reverse global warming” (p. 196), let’s assume that 2800 kg/min will decrease the average temperature of the earth by 2 degrees Celcius.

How much sulfur is needed?

I’m guessing that sulfur dioxide injection would be affected by the law of diminishing returns, but I’m going to assume a linear relationship here. With that assumption, decreasing the average global temperature 36 degrees would require pumping about 100,000 kg of sulfur dioxide per minute. To cause mass extinction, let’s say we have to run this for two years, to make sure that artic and antarctic animals don’t get a chance to stock up on more food in the “summer”. That will take $10^{11}$ kg of sulfur dioxide, or $5*10^{10}$ kg of sulfur. Do we have that much sulfur handy?

It looks like it. The Athabasca Oil Sands in Alberta, Canada have pyramids of sulfur as a waste product of oil extraction. Leavitt and Dubner's book describes pyramids “a hundred meters high by a thousand meters wide” (p. 195), or 30 million cubic meters = $6*10^{10}$ kg S in each pyramid. How many hoses do our five pumping stations need? Each station needs to output 20,000 kg/min, which would require about 100 hoses at each site, or maybe bigger hoses.

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If we assume just two giant pumping stations, at the Athabasca site and at a similar site somewhere in the southern hemisphere, the sulfur dioxide would cover the earth in about 10 days (p. 194). Together, they can freeze the earth for four years, assuming the earth cools off quickly once it can’t receive as much energy from the sun. The sulfur dioxide would settle out of the atmosphere “within a few years” (p. 197).

How much would this cost?

Intellectual Ventures estimates $150 million in opening costs and $100 million per year thereafter for their modest "Save the Earth" proposal (p. 197). Our "Destroy the Earth" operation is about 18 times bigger, so I will guess about 18 times the cost: in the neighborhood of 3 billion dollars for opening costs, and 2 billion dollars to run it per year thereafter: it costs just 7 billion dollars to freeze the earth for two years. Well within the reach of your typical multi-billionaire mad scientist.

But sulfur dioxide is not an element...

For those of you who are going to argue "but sulfur dioxide is not an element", the OP specifically states that he is "Looking for the element that a mad scientist would need the least of", and that element is sulfur. You could just as easily argue that burning hydrogen is not a valid answer because that would produce hydrogen dioxide (water), and water is not an element (at least in modern chemistry). If an element is causing a lot of death, it is probably because it is that element is undergoing a chemical reaction. If my arithmetic is correct, this scenario is too close to plausibility for my comfort.

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