no...
when the phone is on but inactive there's nothing being transmitted, therefore no radiation...
however around every 20 mins or so the phone synchronises with the network/operator for about 2 seconds...
the amount of exposure also depends on the distance you are from the phone...
like if you've got the loudspeaker on and the phone is on the table, you won't get as much exposure compared to when the phone is right by your ear...