The first isotope of plutonium discovered was plutonium-238....

The first isotope of plutonium discovered was plutonium-238. It is used to power batteries for heart pacemakers. A sample of plutonium-238 weighing $2.8 \times 10^{-6} \mathrm{~g}$ decays at the rate of $1.8 \times 10^{6}$ disintegrations per second. What is the decay constant of plutonium- 238 in reciprocal seconds (/s)?

Key Concepts

Avogadro’s Number

Avogadro's number is a constant (approximately 6.02 × 10^23 atoms per mole) used to relate the mass of a substance to the number of constituent particles. It is essential for converting between the macroscopic mass of a sample and the microscopic number of atoms involved in radioactive decay.

Mass-to-Atoms Conversion

Converting a given mass of a radioactive substance to the number of atoms involves using the substance's molar mass and Avogadro’s number. This conversion is crucial for linking macroscopic measurements of mass to the microscopic number of atoms undergoing decay.

Activity

Activity is the measure of the rate at which a sample of radioactive material decays, expressed as the number of disintegrations or decays per unit time. It is directly related to both the decay constant and the number of radioactive atoms present (A = ?N).

Decay Constant

The decay constant is a fundamental parameter in radioactive decay that represents the probability per unit time that a single nucleus will decay. It appears in the exponential decay formula and determines how quickly a sample of radioactive material decays.

Radioactive Decay

Radioactive decay is the process by which unstable nuclei lose energy by emitting radiation. This process is random but follows an exponential decay law where the number of undecayed nuclei decreases over time.

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