Of the radioactive nuclides in Table 25.1 (a) which one has...

Of the radioactive nuclides in Table 25.1
(a) which one has the largest value for the decay constant, $\lambda$ ?
(b) Which one loses $75 \%$ of its radioactivity in approximately one month?
(c) Which ones lose more than $99 \%$ of their radioactivity in one month?

Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous process by which unstable nuclei lose energy by emitting radiation, leading to the transformation into different elements or isotopes. This process is random at the level of individual atoms but follows predictable statistical laws when large numbers of atoms are considered.

Decay Constant

The decay constant, denoted by ?, is a measure of the probability per unit time that a nucleus will decay. It directly relates to the speed of the decay process, with a larger decay constant implying that the substance decays faster, leading to a shorter half-life.

Half-Life

The half-life of a radioactive substance is the duration needed for half of the initial quantity of radioactive atoms to decay. It is intrinsically linked to the decay constant by the relationship T?/? = ln(2)/?, serving as a practical metric for comparing the stability of different isotopes.

Exponential Decay Law

The exponential decay law describes how the quantity of a radioactive substance decreases over time, following the formula N(t) = N? exp(-?t). This law enables the calculation of the remaining fraction of a substance after a given time interval, which is essential for understanding its decay behavior.

Radioactivity Reduction Percentage

The concept of radioactivity reduction percentage quantifies the decline in the activity or number of radioactive nuclei over a specified time period. By relating this percentage to the exponential decay law, one can determine the decaying behavior of isotopes and compare their relative stability.