Question

It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5\() ?\)

Short answer

(a) No, this is not a reasonable suggestion, as radioactive decay is a spontaneous nuclear reaction that does not depend on external factors such as temperature, pressure, or chemical bonding. (b) Radioactive decay does not have an activation energy since it is a nuclear process, not a chemical reaction, and thus doesn't follow the Arrhenius behavior. The rate of decay only depends on the decay constant of the specific element and the amount of the substance, independent of external factors like temperature.

Step-by-step solution

(a) Assessing the reasonability of the suggestion

In order to determine if this suggestion is reasonable, we should understand the process of radioactive decay. The radioactive decay of an element is a process in which an unstable nucleus loses energy by emitting ionizing radiation, such as alpha, beta, or gamma particles. This process is a spontaneous nuclear reaction and does not depend on external factors such as temperature, pressure, or chemical bonding. Because radioactive decay obeys first-order kinetics, it only depends on the decay constant and the quantity of the element. So, suggesting that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactivity decay more rapidly because it will be exposed to much higher average temperatures is not a reasonable suggestion since the rate of radioactive decay does not rely on external factors.

(b) Activation energy of radioactive decay

Activation energy is the minimum amount of energy required for a chemical reaction to occur. The Arrhenius behavior describes the dependence of the rate of a chemical reaction on temperature via the activation energy - as temperature increases, the reaction rate increases. However, radioactive decay is not a chemical reaction but a nuclear process. Thus, it does not have an activation energy and doesn't follow the Arrhenius behavior. The rate of radioactive decay is only dependent on the decay constant of the specific element and the amount of the substance, independent of external factors like temperature.

Key concepts

Strontium-90

Strontium-90 is a byproduct of nuclear reactions, notably those involved in nuclear weapons testing and nuclear power plant operations. It is one of the many isotopes generated during fission processes, where heavier elements are split into lighter ones. Strontium-90 has a half-life of about 28.8 years, which means it takes nearly 29 years for half of a given sample to decay into a more stable form, Yttrium-90. This isotope is particularly concerning due to its radioactive properties and its ability to replace calcium in bones, potentially leading to bone cancer or other disorders.
Understanding Strontium-90 is crucial when discussing radioactive decay and its potential environmental and health impacts. Being placed in a high-temperature environment, like a desert, does not alter its rate of decay, contrary to some beliefs. This is because radioactive decay is solely determined by the isotope's inherent properties and is unaffected by climatic conditions.

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and are distinct from chemical reactions, which involve the rearrangement of electrons around atoms. In a nuclear reaction, new elements can be formed, as protons and neutrons in the nucleus are reconfigured. This can happen through processes such as fission, where the nucleus splits, or fusion, where nuclei combine to form a heavier element.
One critical aspect of nuclear reactions is that they can release enormous amounts of energy, far exceeding what chemical reactions can produce. This energy is due to the conversion of mass into energy, described by Einstein's famous equation, \(E=mc^2\).
Radioactive decay, such as that of Strontium-90, is a type of nuclear reaction characterized by the spontaneous emission of particles or radiation as the unstable nucleus transforms into a more stable state.

Activation Energy

Activation energy is a crucial concept in chemical reactions, representing the minimum energy necessary to initiate a reaction. It's like the initial push needed to start rolling a ball down a hill. In many reactions, if the molecules involved don't have enough energy to surpass this barrier, the reaction won't proceed.
Chemical reactions often follow Arrhenius behavior, which implies that as the temperature increases, the molecules move faster and have more energy, leading to a higher reaction rate. This relationship is described by the Arrhenius equation: \[ k = A e^{-\frac{E_a}{RT}} \] where \(k\) is the reaction rate constant, \(A\) is a frequency factor, \(E_a\) is the activation energy, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin.
While activation energy is a fundamental concept for chemical reactions, it does not apply to radioactive decay, which is a nuclear process occurring independently of external energy supplies.

Spontaneous Processes

Spontaneous processes are natural occurrences that proceed without the need for external energy. An easy way to understand spontaneity is to think about a ball rolling downhill by itself without being pushed. In the context of nuclear reactions, radioactive decay is a perfect example of a spontaneous process.
This type of decay occurs naturally without any external intervention or energy addition. It’s governed by the laws of quantum mechanics and the nature of the unstable nuclides involved.
In spontaneous processes, such as radioactive decay, the system naturally moves towards a more stable state. This makes understanding these processes crucial, especially in fields dealing with energy release or environmental impact, such as nuclear physics and radiochemistry.
Because these processes occur without energy input, environmental conditions like temperature or pressure do not influence the rate of decay, as is the case with Strontium-90, which remains consistent in its decay rate regardless of its surroundings.