Radioactive iodine, ^131 I, with a half-life of 8.0207 days, is used in some forms of medical d

step 1 So in this question, it's given to us that for iodine 131, the half -life is 8 .0207 days. And i

Radioactive iodine, ^131 I, with a half-life of 8.0207...

Radioactive iodine, ${ }^{131} \mathrm{I}$, with a half-life of $8.0207$ days, is used in some forms of medical diagnostics. (a) If the initial activity of a sample is $64.5 \mathrm{mCi}$, what is the mass of ${ }^{131}$ I in the sample? (b) What will the activity be $4.5$ days later?

Key Concepts

Radioactive Activity

Radioactive activity is a measure of the rate at which a sample of radioactive material decays. It is typically quantified in units such as curies (or millicuries) and is defined as the number of decays per unit time. The activity is directly proportional to the number of radioactive atoms present in the sample.

Conversion from Activity to Mass

To determine the mass of a radioactive sample from its activity, one must first calculate the number of radioactive atoms using the relationship A = ?N. Once the number of atoms (N) is known, it can be converted to mass by using the atomic or molar mass and Avogadro’s number. This conversion links the macroscopic measurable quantity (mass) with the microscopic properties of the isotope.

Exponential Decay Law

The exponential decay law mathematically describes the decrease of radioactive activity over time. It is expressed as A(t) = A?e^(??t), where A? is the initial activity, ? is the decay constant, and t is time. This law applies universally to all forms of radioactive decay.

Half-Life

The half-life of a radioactive isotope is the time required for half of the radioactive atoms in a sample to decay. It is a fundamental parameter that characterizes the rate of radioactive decay and is independent of the initial amount of the substance.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. It is a random and spontaneous process that results in the transformation of an element into another element or a different state, with a characteristic rate that is intrinsic to the particular isotope.

Decay Constant

The decay constant, denoted by ?, quantifies the probability per unit time that a given nucleus will decay. It is directly related to the half-life of the substance by the relation ? = ln(2)/T1/2, and it plays a central role in describing the exponential nature of radioactive decay.

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