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Strontium-90 ((90)Sr) is a radioactive isotope that poses significant health concerns due to its beta-emission properties and its similarity to calcium, which allows it to accumulate in bones when ingested or inhaled. It is produced in nuclear fission and found in waste from nuclear reactors and fallout from nuclear testing. The biological half-life of strontium-90—the time it takes for half of the strontium-90 to be expelled from the body—is approximately 18 years, making it a long-term health risk.

Strontium-90 undergoes radioactive decay, a process that is not subject to external factors such as temperature or pressure. This means that regardless of the environment, whether it's a cold Arctic tundra or a hot desert, the decay rate for strontium-90 remains constant, solely determined by its own nuclear properties.

The concept of half-life is fundamental in understanding radioactive decay, as it helps us determine how quickly a radioactive material will decrease in activity. The half-life is defined as the time required for half of the atoms of a radioactive substance to decay. For strontium-90, its half-life is approximately 28.8 years. This means that after 28.8 years, only half of the original amount of strontium-90 will remain; the other half would have decayed into a different element, yttrium-90, through beta decay.

It's essential to recognize that half-life is an intrinsic property of the radioactive isotope and is not influenced by environmental factors such as temperature. This is a key concept that leads us to understand why the decay rate of strontium-90 would not accelerate in a hot desert climate.

Activation energy is a term often found in discussions about chemical reactions. It represents the minimum amount of energy that is required for reactants to transform into products during a chemical reaction. The higher the activation energy, the slower the reaction tends to be, as fewer molecules have sufficient energy to surpass this threshold at a given temperature.

Different from chemical reactions, radioactive decay is a nuclear process that does not require the surmounting of an energy barrier to proceed. It is governed by the principles of nuclear physics rather than chemical kinetics. Therefore, radioactive decay does not feature an activation energy—making this concept inapplicable to the decay of strontium-90 or any other radioactive isotope.

The Arrhenius equation is a critical expression in chemical kinetics, offering a quantitative way to understand how the rate of a chemical reaction depends on temperature and activation energy. Mathematically, it establishes a relationship between the rate constant ((k)), temperature (T), activation energy ((E_a)), and the Arrhenius constant (A).

The equation is given by: \[\begin{equation}k = A~\mathrm{exp}\left(-\frac{E_\mathrm{a}}{RT}\right)\end{equation}\]where R is the universal gas constant. The exp(-E_\mathrm{a}/RT) term shows an exponential decrease in reaction rate with increasing activation energy or decreasing temperature. The Arrhenius equation does not apply to strontium-90's radioactive decay since there is no dependency on temperature and no activation energy barrier to overcome.