There's a lot we don't know about the actinides. On the periodic table, this series of heavy, radioactive elements hangs at the bottom, and includes a host of mysterious substances that don't naturally occur on Earth.

Among this cast of unknowns, berkelium looks to be even stranger than we realised. New experiments with this incredibly rare synthetic element have shown that its electrons don't behave the way they should, defying quantum mechanics.

"It's almost like being in an alternate universe because you're seeing chemistry you simply don't see in everyday elements," says chemist Thomas Albrecht-Schmitt from Florida State University.

For years, Albrecht-Schmitt has studied the complex, radioactive world of actinides, including plutonium, californium, and berkelium.

The latter, discovered in 1949, was named after the Berkeley scientists who first produced it, and one of the reasons it's so little understood, apart from its radioactivity, is because it's so difficult (and prohibitively expensive) to synthesise.

It's estimated that less than 1 gram of the element has been synthesised in the past 50 years. For his latest research, Albrecht-Schmitt was trusted with a whole 13 milligrams of the radioactive metal by the Department of Energy.

That might not seem like much, sure, but it's about 1,000 times more than anyone else has given for major research studies, and it enabled the researchers to observe something they never expected to see.

In a series of experiments over three years, the team engineered various compounds out of berkelium and observed that their electrons behaved unusually.

At the top end of the periodic table, which is dominated by light elements, electrons line up in configurations that are explained by quantum theory.

What Albrecht-Schmitt and fellow researchers discovered is that when it comes to berkelium, and other heavy elements, the principles of quantum mechanics can't actually explain what the electrons are doing.

Instead, it looks like the electrons are governed by Einstein's theory of relativity, which predicts that as objects with mass move faster, they get heavier.

In terms of the electrons in berkelium, the thinking goes that as the electrons begin to move at extremely fast speeds around each atom's highly charged nucleus – at up to significant fractions of the speed of light – this causes them to become heavy, and behave in ways that defy a quantum explanation of events.

"When you see this interesting phenomenon, you start asking yourself all these questions like how can you make it stronger or shut it down," says Albrecht-Schmitt.

"A few years ago, no one even thought you could make a berkelium compound."

The work builds upon previous research involving berkelium compounds published last year by the same team, which also teased that berkelium was "electronically different than what people expected".

As this body of work builds, it's yet more evidence that berkelium, like the periodic table itself, is something that's almost impossible to pin down – and it remains to be seen just how far these mysterious actinides will make our best theories bend or break.

"What this really gives us is an understanding of how chemistry is changing late in the table," Albrecht-Schmitt explained last year.

"The purpose is to understand the underlying chemistry of the element. Even after having [berkelium] for almost 70 years, many of the basic chemical properties are still unknown."

The findings are reported in the Journal of the American Chemical Society.