translation - What is the rule in assigning kanji to a new word?

For example, Hydrogen was found by Henry Cavendish. Mr. Cavendish was not a Japanese and I'm pretty sure he won't bother inventing the name for Hydrogen in all the languages in the world, especially in a language that doesn't use the same set of alphabet as the languages he mastered. In fact, he didn't even name it. It was Antoine Lavoisier who gave the name Hydrogen. Google translate translates Hydrogen as 水素 (すいそ).

What I want to know is how the kanji 水素 was chosen to represent Hydrogen? What are the rules that one must follow in assigning kanji to a newly found thing/word? Or one can just assign whatever kanji he wants much like how in English you can just assign whatever name you want to something you found, like is the case with Big Bang being named Big Bang even when it is not an explosion.

Answer

See this article: Chemical elements in East Asian languages

In general, Japanese experts today no longer create totally new kanji compounds. They use kanji only when a combination of existing compounds (words) can directly represent the original phrase. For example, deep learning is translated either as ディープ・ラーニング or 深層学習, where 深層 ("depth") and 学習 ("learning") are both very old words.

Old Japanese people (approx. 100-150 years ago) tended to create various new kanji compounds based on the characters' meanings, as they rapidly learned many Western concepts. Examples include 文明 ("literacy" + "enlightenment" = "civilization"), 電話 ("electricity" + "talk" = "phone"), 物理 ("thing" + "reason" = "physics"), 野球 ("field" + "ball" = "baseball"). Some of these new words were actually reverse-imported to Chinese. See wasei-kango. I don't believe there is a technical term that was assigned purely random kanji in those days.

Some traditional chemical element names such as 水素/臭素 were created in the same manner ("water" + "element" = "hydrogen", "stench" + "element" = "bromine"). I think the etymology of 水素 is fairly straightforward. However, chemical elements discovered relatively recently are simply transliterated using katakana. For example, Neptunium is translated as ネプツニウム in Japanese. On the other hand, Chinese people still keep inventing new compounds for new Western names/concepts (See this and this). They are even inventing a new kanji for each new chemical element (Neptunium is 镎 in Chinese).