<p>Good luck! I’d wait to hear from these professors before sending out other emails (wait at least a week). Some may never get back to you, especially if they have spam blockers, but since you’re the one pursuing this internships, it’s rude to say, “Oh, thanks but no thanks for your consideration.” This isn’t a job hunt; you’re asking unsuspecting professors to take time out of their day to consider your offer and respond.</p>
<p>Best of luck!</p>