Tritium, or hydrogen- 3, is prepared by bombarding lithium-6...

Tritium, or hydrogen- 3, is prepared by bombarding lithium-6 with neutrons. A $0.250-\mathrm{mg}$ sample of tritium decays at the rate of $8.94 \times 10^{10}$ disintegrations per second. What is the decay constant (in $/ \mathrm{s}$ ) of tritium, whose atomic mass is $3.02$ amu?

Key Concepts

Conversion from Mass to Number of Nuclei

To determine the decay constant from the activity, it is necessary to calculate the total number of radioactive nuclei present in a given mass. This involves converting the mass of the sample to moles using the atomic mass, and then converting moles to number of nuclei using Avogadro's number. This conversion is essential to bridge the gap between the measurable mass and the number of atoms undergoing decay.

Activity

Activity is defined as the number of nuclear disintegrations per unit time, typically measured in decays per second (Becquerels). It quantifies how quickly a radioactive sample is decaying. In calculations, it is often equated to the product of the decay constant and the number of atoms, linking microscopic decay events to a macroscopic observable.

Radioactive Decay

This is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. In the context of the problem, tritium decays over time, and each decay event contributes to the overall activity of the sample. The process is statistical in nature and is governed by principles that determine the rate of decay.

Decay Constant

The decay constant is a fundamental parameter that represents the probability per unit time that a nucleus will decay. It is a key factor in the exponential decay law and is used to relate the number of undecayed nuclei to the activity of the radioactive material. A higher decay constant indicates a faster rate of decay.

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