Technetium-99m ( 99mTc ) is commonly used in nuclear medicine imaging. A patient is to be injected at 09:00 h, and the scan will start exactly 4.0 h later. For satisfactory image quality, the activity of 99mTc inside the patient must be 5.0mCi at the moment the scan begins. The physical half-life of 99mTc is 6.02h.
(i) Calculate the decay constant of 99mTc.
(ii) Determine the minimum activity that has to be injected at 09:00 h so that the required activity is available at 13:00 h.
(iii) The maximum permissible activity that may be injected is 10mCi. State whether the value obtained in part (ii) is within this safety limit and give a brief justification.