Write a reminder about a possible undergraduate project
I'm not in the best position to advise you, but, perhaps, he/she hasn't answered you back, because he/she was busy to do so.
Thus, you definitely should e-mail back. Quoting a professor, maybe something like this:
"My e-mail server has been acting up lately, so I'm not sure whether my previous message was delivered properly; here it is again, just in case. Thank you!"
Read the following before:
- Email Writing Tips
- Read This Before Cold-Emailing Me
- Examples of Good and Bad Cold Emails
Best of luck!
I'm afraid this is really subjective to the Professor you are approaching. If he/she is well known in the field of study, as you said, then it's likely he/she is having many similar enquiries and can't respond to all of them. Also as others have said - Professors don't always reply immediately. In either case, sending a second e-mail doesn't hurt and the Prof. won't generally get annoyed at you for sending "already a second email".
In my opinion, there is also nothing wrong with contacting the PhD / PostDoc person most relevant to your question. Don't spam the entire lab, but write to someone and suggest that you asked the Professor earlier, but didn't get a reply (yet) - probably because he/she is too busy.
In our lab it is common that these sort of e-mails do get forwarded (from the Prof.) to the entire lab - you won't know about this, but I guess it's not uncommon.
Since, as you said, this is concerning a Masters Thesis and you are not at the same university as the Professor, unfortunately, your enquiry will be pretty low on the priority list. Why? Because, the Professor has to attend his/her students at the local university first. They also have to write their Masters Thesis and the Professors have an obligation to take them on (at least where I went to university). So don't be disappointed, but don't expect this to actually go anywhere.
[EDIT]
Depending on the popularity of the Professor, you may also have to assume that they never read your mail in the first place, because they simply can't read all their mail. In an ideal world, they would hire assistants / secretaries to help out, but that costs money and not every Professor ca do that.
So, a probably not uncommon approach for Professors is, to simply delete all mail that is older than X days, because they can't possibly go through them and if it was important, the person would have written back or called. In my own experience, even the PhD students and PostDocs wouldn't always get a reply from their own Professor, unless they send the same mail 3-4 times. Of course that's counterproductive, but if it's the only way to get a reply, you don't have a choice.
In the end I would include "Reminder" or something like that in the Subject-Line. The Professors I know are more concerned about efficiency, than etiquette. They want to get to the point quickly and don't have to read through apologies.
The most polite way I would come up with would be to say something like:
Please allow me to remind you of my request...
No need to tell Professors that they are busy ;) I also often see the request to forward something to their lab, actually being honoured. But as I said before, if you can reach one of the lab members - they all conduct their own research and surely have conversations with different people all the time - no need for the Professor to approve.
Let me start with my personal experience from similar situations: professors rarely respond to emails of this nature.
This is partly because many people bombard professors' inboxes with emails about joining their research group every day. So it is highly likely that he has not read your email carefully or at all.
Here are my suggestions:
At the beginning of your email mention that you tried contacting him before. This simple act has been very effective in my experience. Possibly because the professor might take time to read your email more carefully knowing that you've been trying to contact him for a while. I sometimes mention that I understand that they get a lot of emails from potential applicants every day and that I suspect that they may have missed my previous email.
Choose the topic of your email wisely. If the topic says something like "interested in your research" it would garner less interest from the professor than if you mention that you are interested in some sort of collaboration on a research project.
Try to keep your email short, and try to put the information that may make him interested at the beginning of the email. For example, it may help to let him know that you are not looking for admission to their university or a funding opportunity.
Since this person is likely the corresponding author on the papers published by his group you could use this for a different approach. For example, read the articles he has published that are close to the research project you wish to work on and ask questions you may have in that context. Maybe this could be a way to open the communication line.