A typical banana contains 400 mg of potassium, of which a small fraction is the radioactive isot

step 1 Okay, so the first thing to do here is find the number of nuclei of potassium 39. So n of K3919

A typical banana contains 400 mg of potassium, of which a...

A typical banana contains 400 $\mathrm{mg}$ of potassium, of which
a small fraction is the radioactive isotope $\frac{40}{19} \mathrm{K}$ ( see
Appendix: Selected Isotopes). Estimate the activity of an
average banana due to $\frac{40}{19} \mathrm{K.}$

Key Concepts

Radioactive Activity

Radioactive activity is the measure of the number of nuclear decays that occur per unit time in a radioactive substance. It is typically measured in becquerels (decays per second) or curies, and its calculation requires knowing the number of radioactive nuclei present and the probability per unit time that any one nucleus decays.

Decay Constant

The decay constant represents the probability per unit time that an individual nucleus will decay. It is directly related to the half-life of the isotope by the relation ? = ln(2)/T?/?, and it plays a crucial role in determining the activity of a radioactive material.

Half-Life

The half-life of a radioactive isotope is the time required for half of the nuclei in a sample to decay. This characteristic time scale is essential in calculating the decay constant and understanding the rate at which a radioactive substance transforms into its daughter products.

Isotopic Abundance

Isotopic abundance refers to the fraction of an element's atoms that are a specific isotope. In mixtures where only a small fraction of the element is radioactive, this quantity is crucial for determining the number of decaying nuclei present and, consequently, the overall activity.

Mass-to-Mole Conversion

Conversion from mass to number of atoms is achieved by using the molar mass of the element along with Avogadro’s number. This step is essential when calculating the total number of radioactive nuclei present in a given sample, which then allows for the estimation of its activity.

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