You will lose up to 24 minutes of full productivity, according to several different pieces of research. For example: "A study by Microsoft researchers tracking the email habits of co-workers found that once their work had been interrupted by an email notification, people took, on average, 24 minutes to return to the suspended task" [1].

The issue is the cognitive load introduced by task switching. You may not realize it on the surface, but breaking away each time to write a reply (or even to a lesser extent just the mere fact that you are now notified there's a message waiting) is causing a huge distraction for your brain, and slowing down your "real" work.

[1] Paul Hemp. 2009. "Death by information overload," Harvard Business Review 87(9).

A good five minutes is "Where was I?"

If you get interrupted a lot it helps to take notes on a pad, kind of use it as your "stack" and just list out what you're doing so when you're done you can go back to that frame of mind more easily.

You're interrupting whatever else you were doing, for a start. That'll throw your efficiency off.

Plus composing a reply is time-consuming in itself- you often need to look up something, check a document, etc. etc.

The time that it takes to get back into the flow of whatever you were doing.

http://www.atlassian.com/time-wasting-at-work-infographic

Not sure if you can actually be "100%" productive in that full work day -- but it certainly is more effective to do your work efficiently, and then go home and have proper time off, doing the same amount of work in less time. Six hour work days doesn't seem so bad if you're average worker is only working five hours out of an eight hour day anyway.