The only way to leave behind traces of your radiation is to deposit fluids on objects (urine, sweat, tears, saliva, snot, etc.). This is why they say to wash your hands completely after using the bathroom, not to share eating utensils, to do laundry separately, dry kissing only, etc in the beginning when you are dumping loads of RAI, especially through urine. So they will probably tell you not to share the telephone for the first 4 to 7 days when you are especially "hot" and to wipe things down that you can. If you can avoid being sweaty on objects, that's great. As for the timetable, when you can quite being careful, I'd ask the person who gives you the RAI pill (usually there is a radiation safety person that goes over the "rules"). If you contaminate anything, it will be free of radiation in 80 days so you can just put it somewhere for a couple months and then get it back....All of the high risk of contamination is in the first week, depending on your dose.