Half-life definition refresher: the time required for half of the __________ of a radioactive sample to undergo decay is called the half-life of that nuclide. Fill in the most precise word.

Introduction / Context:
Radioactive decay is a stochastic process at the level of individual nuclei but produces a characteristic exponential law for large ensembles. The half-life is a core parameter in nuclear science, radiological protection, geochronology, and medical imaging, defining the time at which half the original radioactive nuclei have decayed.

Given Data / Assumptions:

• We are discussing a specific radioactive nuclide.
• Terminology must be precise: decay refers to transformations of nuclei.
• Electrons, protons, and neutrons inside other contexts are not what “half-life” counts.

Concept / Approach:
The exponential decay law is N(t) = N0 * exp(−λt), where N(t) is the number of undecayed nuclei at time t and λ is the decay constant. The half-life t_1/2 satisfies N(t_1/2) = N0/2, which leads to t_1/2 = ln 2 / λ. The definition centers on the number of undecayed nuclei in the sample—neither electrons nor free protons are being “consumed” in the definition.

Step-by-Step Solution:
State the decay law for nuclei: N(t) = N0 * exp(−λt).Define half-life via N(t_1/2) = N0/2.Solve for t_1/2: t_1/2 = ln 2 / λ.Identify the quantity halved: the count of undecayed nuclei.

Verification / Alternative check:
Any standard text defines half-life with respect to a population of identical radioactive nuclei in a sample. Derived quantities like activity A(t) = λN(t) inherit the same time dependence.

Why Other Options Are Wrong:
Electrons/protons/neutrons: Not the counted entities in half-life definition; decay transforms nuclei.Atoms in the entire universe: Irrelevant and nonspecific.

Common Pitfalls:
Confusing “half-life of activity” with “half-life of mass”; while proportional for a single nuclide, activity is a rate variable derived from N(t), which counts nuclei.

Final Answer:
nuclei