Question

You go to the doctor and he gives you 12 milligrams of radioactive dye. After 12 minutes, 4.5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.

Answer 1

x=xo xt, e- is know, Radioactive decay is 1st order reaction. And it follows the rile, (where to is the initial amount of the material and amount after time to Here a is measured in miligrams and t in 'is a constant, called the delay Constanta Given that o 121 and a= 4.5 when t=12. So, 4.5= 12 xe -12 > -12= 3) 12 -0.9808 + 0.817. (approx.) Let T be the time when 2. In (4.5 7 2 = 12:6-AT → 2T = = ln 6. → Ta en 6 ~ 21.9309. ~ need to spend 122 minutes Counded to minutes) to Thus, nearest to avoid sound of the alarm)