The most radioactive of the isotopes of an element is the...

The most radioactive of the isotopes of an element is the one with the largest value of its (a) half-life, $t_{1 / 2}$
(b) neutron number, $N ;$ (c) mass number,
Z;
(d) radioactive decay constant, $\lambda$

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Key Concepts

Radioactive Decay Constant

This is a value that quantifies the probability per unit time that a nucleus will decay. A higher decay constant means that each nucleus is more likely to decay quickly, leading to a higher overall radioactivity. It is mathematically related to the half-life by the expression ? = ln(2) / t?/?, thus serving as a direct measure of the intrinsic rate of radioactivity.

Half-Life

The half-life of a radioactive substance is the time required for half of its nuclei to decay. This parameter inversely relates to the decay constant, meaning a shorter half-life corresponds to a higher decay constant and faster decay rate, indicating greater radioactivity. It is one of the central measures in understanding the temporal behavior of radioactive decay.

Nuclear Isotopes

Nuclear isotopes are variants of a chemical element that differ in the number of neutrons, and consequently in mass number, while retaining the same number of protons. Although differences in neutron number and mass number affect nuclear stability and decay characteristics, the most direct measure of an isotope's radioactivity is determined by its decay constant and half-life rather than simply by these nuclear composition factors.

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