which one of those two sentences is correct
"The professor called on me for question 1"
"The professor called me on for question 1"
The first one is correct; the second is not. Unfortunately it's not so simple as "call on" never being splittable though, with one meaning it actually must be split. Unfortunately the two meanings are very different and one is quite negative, so the potential for misunderstanding is not insignificant here.
I'm not entirely sure how to explain the grammar of this, but I can explain the usage of each version.
A. Call on someone
This either means to ask for a response to a question or (old fashioned) to visit either in person or by telephone. In both cases the thing that I emphasizing with "call on" is the person who is the target of the calling and the preposition "on" is targeting a particular person.
I try to call on as many students as possible in class so that I get a variety of responses.
Jane called on Dorothy after hearing that she had fallen ill.
B. Call someone on something
This is used when someone is being deceptive, often habitually, and we want to describe to someone else how we confronted the deception. The object of "on" is the deception itself, not the person who is lying.
Ex: My friend John likes to tell tales about how great he is, but they get tiresome at times. I'm now telling my other friend Sue about my confrontation with John regarding his lies.
After a while, I couldn't take any more of John's nonsense, so I called him on it. He didn't have any response, and I don't expect that he will stop, but it felt good to get that off my chest.
Ex: I have evidence that my girlfriend is cheating on me and I'm talking with another person about how to address it.
I don't know how long she has been seeing this man, but she has to have been lying to me for months. I think that tonight I'm going to just call her on it and see if she is decent enough to finally tell me the truth.
Was that question about some security? Some great thing that required your utmost attention? Did professor need emergency help from you?
If any of these questions' answer is 'no', you are not supposed to 'call on' for that question!
the use of 'call on' are different. You may call on for some professional help, call on for some official help etc. There are many uses of 'call on' but as user3169 states, none of them seems to be closer to your concern.
I'm not sure what exactly do you mean, but I'd generally say this -
The professor asked me question #1