Timely answers to academic e-mails and internet addiction
What's considered a timely response depends on context.  A response could be expected within hours, days, or weeks, depending on the email.  What I think is important is that both parties are clear on expectations.  

For normal academic activities, I would say checking emails twice a day is generally sufficient.  Academics are often busy with classes and meetings throughout the day, so it's generally understood (at least between faculty, though not always by students) that you might not read or respond to an email within an hour.

However, it sounds like your PI expects you to check email more frequently than you do, so it's probably worthwhile mentioning that you only check email a few times a day (if asked why, just say so it doesn't distract you too much from your work).  Then you can see if your PI is happy with calling you or seeing you in person if it's something urgent.  If not, and PI really wants you to check email constantly, maybe you can set up something where you will only see emails from your PI (e.g., forward them to another email that you use for nothing else).

Similarly, if there are other people that seem to be expecting immediate responses from you, just maybe add a "PS" in your reply about how often you check email.  I don't think most people will be upset if they know your habits.