Correct Answer - Option 2 : Only II
Here, it should be clear that both the sentences show contrast i.e. first part shows that something was known and still there has been no action taken in the second part of the sentence.
So the correct word that would join these sentences is though.
The muon is an elementary particle similar to the electron, with an electric charge
While is used in a sentence to show actions that happen simultaneously.
Being is grammatically incorrect in the sentence structure
Correct Sentence:
Though it was known that thunderstorms had an effect on muon intensity, it had not been probed in detail earlier.
Hence, option 2 is the correct answer.