Since the professor has asked you to write the paper, I presume that he does not intend to be the first author. Almost no professor will want to be the first author of a paper whose text is obviously written by a student. The first author is usually presumed to be the author of the text, i.e., the person who actually wrote the text, and very few professors would sign a substandard text as the first author.
You can have a look at the professor's publication list to determine whether he often lets his students be first authors. If he does, he is likely to do the same in your case.
There is a simple method to remove the uncertainty about the order of authors. Prepare some very initial draft of the paper: write the title, abstract, and a few paragraphs of the main text, and write the authors in the order you think is most fair. Then email this initial draft to your professor together with some question about the draft. The professor will open the draft and see the order of the authors. If he makes no objection against the order of the authors, consider it negotiated. Later you can always refer to that email and the absence of objections. It is entirely normal to include the author list in a paper draft; moreover, failing to do so is rather weird, especially if you use an article template taken from the journal website, as such templates have a special place for the author list.
Do it early, not late. I know one postdoc who wrote a very good paper, in which he put himself in the fist position and his professor in the second, and then sent it to his professor, who then made only one correction: he swapped the positions. The actual contribution by the professor was nothing but funding the postdoc's salary. The postdoc was pissed off, but simply swallowed it because he needed a prolongation of his postdoc contract and was unable to take postdoc positions in other cities and countries for family reasons. If the postdoc had known in advance that he was going to be the second author, he would have at least invested less effort in that particular paper. Furthermore, if the postdoc had used the above described method in advance (i.e., in the very initial stage of writing the paper), the professor would possibly not have swapped the positions, because he would have known that such an action would strongly demotivate the postdoc and result in a paper of a worse quality.
Please note that students generally lack writing skills, so your professor well may have to re-write the paper or invest a lot of time and effort to teaching you how to write papers. If this happens, it may be fair to put him in the first position. If he really invests a lot of time and effort and suggests putting him in the first position, don't strongly argue with him, especially as you need a recommendation letter.