Arnold was the fifth woman in history to be awarded the prize.
Wednesday's prize went to Goodenough; M. Stanley Whittingham, 77, a British-American chemistry professor at Binghampton University, the State University of NY; and Japan's Akira Yoshino, 71, of Asahi Kasei Corporation and Meijo University.
Rechargeable lithium-ion batteries can be found in pretty much everything from mobile phones to electric vehicles, and can store significant amounts of energy from solar and wind power. The three scientists will split that cash prize equally.
The groundwork for lithium-ion batteries was laid down during the height of the oil crisis in the 1970s, with Whittingham looking to develop energy technologies that weren't reliant on fossil fuels. Then he came across Goodenough's use of cobalt oxide cathodes in the design of rechargeable batteries and managed to create the first commercially viable lithium-ion battery in 1985. He holds the original patent on the concept of the use of intercalation chemistry in high-power density, highly reversible lithium batteries - work that provided the basis for subsequent discoveries that now power most laptop computers - and his research has been called 'world-leading'.
Lithium-ion batteries are also an important technology in enabling the world to move away from fossil fuels.
The cash prize comes with a gold medal and a diploma that are received at an elegant ceremony in Stockholm on December 10, the anniversary of the death of prize founder Alfred Nobel in 1896, together with five other Nobel winners.
Goodenough is known worldwide for his work on developing lithium-ion batteries and in the early morning hours on Wednesday, he was one of three who won the Chemistry prize.
William G. Kaelin Jr. of Harvard Medical School and the Dana-Farber Cancer Institute, Gregg L. Semenza of Johns Hopkins University and Peter J. Ratcliffe at the Francis Crick Institute in Britain and Oxford University won the prize for advances in physiology or medicine. Scientific breakthroughs are rarely - if ever - a solo endeavour and it is absolutely fitting that this year's Nobel Prize for Chemistry should be shared in this way.
The prize turned out to be a bit of a family affair among the researchers: Yoshino said he visits Goodenough almost every year in Texas. I know it is the week of Nobel Prize, but I didn't pay attention.
Two literature laureates are to be announced Thursday, because last year's award was suspended after a scandal rocked the Swedish Academy.