A human body eliminates certain substances following a law analogous to radioactive decay. When technetium is administered to a human body in some chemical form, half of the substance is excreted in 24 hours . An injection of ⁹⁹ Tc is given to a patient. This specific isotope undergoes radioactive decay with a half-life of 6 hours . Immediately following the injection, the activity from the body is measured to be 6 C

Step-by-step solution

The effective decay constant _ eff for a substance undergoing both biological excretion and radioactive decay is the sum of the biological decay constant _b and the physical decay constant _p . _ eff = _b + _p Since = 2 T_ 1/2 , the effective half-life T_ eff is given by: 1 T_ eff = 1 T_b + 1 T_p Given the biological half-life T_b = 24 hours and the physical half-life T_p = 6 hours : 1 T_ eff = 1 24 + 1 6 = 1 + 4 24 = 5 24 hours ⁻¹ T_ eff = 24 5 = 4.8 hours The initial activity is A₀ = 6 Ci and the final activity i