State whether the following statements are true or false. If false, explain why. (a) The dose equivalent is lower than the actual dose of radiation because it takes into account the differential effects of different types of radiation. (b) Exposure to \(1 \times 10^{8} \mathrm{~Bq}\) of radiation would be much more hazardous than exposure to \(10 \mathrm{Ci}\) of radiation. (c) Spontaneous radioactive decay follows firstorder kinetics. (d) Fissile nuclei can undergo fission when struck with slow neutrons, whereas fast neutrons are required to split fissionable nuclei.

When considering the impact of radiation on the human body, it's crucial to differentiate between the actual dose absorbed and the dose equivalent. The dose equivalent, measured in sieverts (Sv), assesses the biological effect of radiation, not just the amount absorbed. It derives from the absorbed dose, measured in grays (Gy), by factoring in the type of radiation and its relative biological effectiveness (RBE).

For instance, alpha particles have a higher RBE compared to beta particles, meaning that an absorbed dose of alpha radiation can lead to a significantly higher dose equivalent compared to the same absorbed dose of beta radiation. This adjustment ensures that the dose equivalent reflects the actual risk and damage posed to biological tissue, which is why the statement implying that the dose equivalent is universally lower than the actual dose is incorrect; in reality, the dose equivalent can be equal to or exceed the absorbed dose, contingent on the radiation type.

Understanding radioactivity entails familiarity with its measurement units. The becquerel (Bq) and the curie (Ci) both quantify radioactivity, but they represent vastly different scales. One Bq corresponds to one nuclear decay per second, while one Ci is equivalent to approximately 37 billion (\(3.7 \times 10^{10}\) Bq) decays per second. Hence, comparing different volumes of radioactivity demands careful unit conversion.

When faced with an erroneous comparison of units, like in the given exercise, it's essential to emphasize that 1 Ci is significantly higher than 1 Bq, and consequently, 10 Ci (\(3.7 \times 10^{11}\) Bq) represents a much greater amount of radioactivity than 1 times 10^8 Bq. This fundamental knowledge prevents the misinterpretation and underestimation of radiation exposure risks.

Radioactive decay is governed by first-order kinetics, a core concept in chemical kinetics and nuclear chemistry. This type of decay signifies that the rate at which a radioactive substance disintegrates is directly proportional to the amount of the substance present at any given moment. Symbolically, it follows the equation: \[ -\frac{dN}{dt} = kN \]
where \( N \) is the number of undecayed atoms, \( t \) is time, and \( k \) is a constant specific to the substance known as the decay constant. An essential aspect of first-order kinetics in radioactivity is the concept of the half-life, the time required for half of the radioactive atoms in a sample to decay. This constant rate of decay means that regardless of how much radioactive material you start with, it will always take one half-life for half of the material to decay, underscoring the predictability and constancy of the decay process.

The terms 'fissile' and 'fissionable' are crucial in nuclear physics, particularly concerning nuclear reactors and weapons. Fissile nuclei, such as Uranium-235 and Plutonium-239, are special because they can sustain a nuclear chain reaction when bombarded with thermal (slow) neutrons. This property is fundamental for nuclear reactors, where controlled chain reactions provide a steady source of energy.

On the contrary, fissionable nuclei can also undergo fission but usually require fast neutrons to do so. Fissionable materials, like Uranium-238, are not capable of sustaining a chain reaction with slow neutrons alone. Understanding the distinction helps clarify this misconception and highlights the unique quality of fissile materials in supporting the self-sustaining chain reactions crucial for nuclear power and weaponry.