Radioactivity, Half-Life & Inverse Square Law - GCSE & A-level Physics (full version)

This paragraph introduces the concept of radioactive decay using the analogy of a tower of bricks, where adding more bricks makes it unstable and prone to collapse. It then relates this to atomic nuclei, explaining that a nucleus with more neutrons, like carbon-14, is less stable and more likely to decay. The paragraph defines isotopes as elements with different numbers of neutrons, hence different mass numbers. It also introduces the decay constant (lambda) as the probability of decay per second, and explains that while the decay of an individual nucleus is random, the decay of a large number of nuclei can be predicted statistically. The concept of half-life is introduced as the time it takes for half of a radioactive substance to decay, with radioactivity measured in counts per second (Becquerels). The paragraph concludes with a discussion on how radioactivity decreases over time and how it can be represented graphically, showing exponential decay.

This paragraph delves into the graphical representation of radioactive decay and the process of determining half-life from a graph. It explains how to calculate the half-life by observing the time it takes for the activity to decrease by half. The paragraph also addresses how to handle situations where you're given numerical data instead of a graph, emphasizing the importance of identifying the number of half-lives that have passed based on the reduction in radioactivity. It provides examples of how to calculate the half-life when given initial and final activities over a certain period, considering the effects of background radiation. The summary also touches on the mathematical representation of exponential decay, introducing the decay constant and its relation to the remaining activity and the number of undecayed nuclei.

This paragraph provides a deeper mathematical understanding of radioactive decay. It starts by defining the symbols used in decay equations, such as the activity (a), decay constant (lambda), and the number of undecayed nuclei (n). The relationship between activity and the number of remaining nuclei is expressed through the equation a = lambda * n, highlighting that activity is proportional to the number of nuclei and the probability of decay. The paragraph then explains how to derive the equation for the decay of nuclei over time, involving integration and the natural logarithm, leading to the final equation n = n0 * e^(-lambda * T), where n0 is the initial number of nuclei. It also discusses the concept of half-life (T1/2) and time constant (Ts), explaining how they relate to the decay constant and the remaining activity or mass. The paragraph concludes by emphasizing the importance of practice in applying these concepts to solve problems related to radioactive decay.

The final paragraph discusses the practical aspects of measuring radioactivity, particularly gamma radiation, using a Geiger counter. It explains that while it's theoretically possible to measure radiation by creating a spherical detector, in practice, a Geiger counter is used to measure counts per second. The paragraph introduces the concept of intensity, which is the amount of radiation per unit area, and explains that intensity is inversely proportional to the square of the distance from the source, known as the inverse square law. It provides examples of how moving the detector further away from the source reduces the intensity of radiation and gives a formula to calculate the new intensity when the distance changes. The paragraph concludes with a reminder to consider the inverse square law when measuring radiation at different distances from the source.