An evil genius was present at your birth. Unbeknownst to you or your mom, you we

Question

An evil genius was present at your birth. Unbeknownst to you or your mom, you were injected with 100 cubic centimeters (cc) of a docile radioactive material as an experiment the moment you were born. You have recently discovered the unauthorized addition and want to know how much of the substance is still left in your body. You craftily figured out the formula for deterioration of the substance and are ready for some answers. First we had to find our age. so 26years and 112 days old before solving the question

Explanation / Answer

The formula for decay of a radioactive material is Qt = Q0 e-kt, where k is a positive constant, Q0 is the initial quantity (at time t = 0) and Qt is the quantity left after a lapse of time t. Now, k can be determined if the half-life (the time T in which the initial quantity decays to half) is known. Then Qt = Q0/2 so that e-kT = ½ or ekT = 2 so that kT = ln(2) (ln denotes natural log). Thus k = (1/T)ln(2). Now, knowing the initial quantity, the constant k (only if the name of the radioactive material and/or its half-life T is known), and the formula for decay, we can compute the quantity left after 26years and 112 days ( on substituting t = 26years and 112 days).

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