Radon-220 is radioactive, and decays into polonium- 216 by...

Radon-220 is radioactive, and decays into polonium- 216 by emitting an alpha particle. This is a firstorder process with a rate constant of $0.0125 \mathrm{~s}^{-1}$. How many alpha particles per second will be emitted by one picogram of ${ }^{220} \mathrm{Rn}$ inhaled on a particle of dust?

Key Concepts

Mass-to-Mole Conversion and Avogadro's Number

Converting a small mass of a substance into the number of particles involves using its molar mass and Avogadro's number. This process translates the mass (e.g., one picogram) into moles, and then into the actual count of atoms or molecules, which is essential for calculating quantities like activity in radioactive decay scenarios.

Activity Calculation

Activity refers to the number of decays or disintegrations per unit time, typically measured in becquerels (decays per second). For a radioactive substance undergoing first-order decay, the activity is calculated by multiplying the decay constant with the number of radioactive nuclei present, illustrating the link between the microscopic decay process and a measurable macroscopic quantity.

Decay Constant (Rate Constant)

The decay constant, often represented by the symbol lambda (?), quantifies the probability per unit time that a nucleus will decay. It is central to the exponential decay law, which relates the number of remaining radioactive nuclei to time, and is used to calculate the activity of a radioactive sample.

First-Order Kinetics

In first-order kinetics, the rate of a process is directly proportional to the concentration or number of reactant particles present. In radioactive decay, this means that the probability per unit time for any single nucleus to decay is constant, and the overall rate of decay is given by the product of the decay constant and the number of undecayed nuclei.

Radioactive Decay

This is the process by which unstable nuclei spontaneously transform into a more stable configuration by emitting particles and energy. It is a fundamental concept in nuclear physics describing how a parent nucleus loses mass and energy to form a daughter nucleus, often producing ionizing radiation such as alpha particles.

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