To determine which statement is correct regarding the disintegration of a nucleus, we need to delve into the principles of radioactive decay and half-lives. Let's analyze each statement one by one.
Evaluating the Statements
1. The probability of a nucleus disintegrating is lower in the first half and greater in the second half.
This statement is incorrect. The probability of a nucleus disintegrating is constant over time. Radioactive decay follows a statistical process where each nucleus has a fixed probability of decaying per unit time, regardless of how long it has existed.
2. The probability of a nucleus disintegrating is constant for all time.
This statement is correct. In radioactive decay, each nucleus has a constant probability of disintegrating, which is defined by its decay constant. This means that the likelihood of decay does not change as time progresses. For example, if a particular isotope has a decay constant of 0.1 per year, every year, there is a 10% chance that any given nucleus will decay, independent of how long it has been around.
3. Every nucleus must disintegrate during the average life of the population.
This statement is misleading. While it is true that on average, a certain fraction of a population of radioactive nuclei will decay over a given time period (related to the half-life), it does not mean that every single nucleus will decay. Some nuclei may remain stable for much longer than the average life of the population.
4. The disintegration rate of an element in its isolated and combined state remains the same.
This statement is generally true. The decay rate of a radioactive isotope is a property of the nucleus itself and does not change whether the element is in isolation or part of a compound. However, external factors like extreme pressure or temperature can sometimes influence decay rates, but these effects are typically negligible under normal conditions.
Summary of Findings
Based on the analysis, the correct statement is the second one: "The probability of a nucleus disintegrating is constant for all time." This reflects the fundamental nature of radioactive decay, where each nucleus behaves independently and has a fixed probability of decay that does not change over time.
Understanding Radioactive Decay
To further illustrate this concept, consider the analogy of a game of dice. If you roll a die, the probability of rolling a six is always 1 in 6, regardless of how many times you have rolled it before. Similarly, each radioactive nucleus has a constant probability of decaying, independent of its past behavior.
In summary, when studying radioactive decay, it's essential to remember that the decay process is random and governed by statistical laws, leading to the conclusion that the probability of decay remains constant over time.
