A certain Geiger counter is known to respond to only 1 of every 1000 radiation events from a sample. Calculate the activity of each radioactive source in curies, given the following data: (a) 591 clicks in \(100 . \mathrm{s}\); (b) \(2.7 \times 10^{4}\) clicks in \(1.5 \mathrm{~h}\); (c) 159 clicks in \(1.0 \mathrm{~min}\).

The Curie (Ci) is the fundamental unit of radioactivity, named in honor of the pioneer researchers Marie and Pierre Curie. It quantifies how many atomic nuclei in a material are decaying each second. Precisely, 1 Curie represents the radioactivity equivalent to that of 1 gram of radium-226, which corresponds to approximately 3.7 x 10^10 radioactive disintegrations per second. Despite being superseded by the becquerel (Bq), which is the SI unit of radioactivity where 1 Bq equals 1 disintegration per second, the Curie remains in use due to its historical significance and is still commonly used in certain fields like medicine.

In the context of radioactive measurements, efficiency is pivotal when using detection instruments, like a Geiger counter. Efficiency refers to the capability of the counter to detect the actual number of disintegration events occurring. For instance, if a counter registers only 1 response per 1000 events, this does not imply the counter is ineffective but rather it illustrates the necessity to adjust reported counts to reflect true activity. By understanding the efficiency, one can correct for the underreporting and calculate a more accurate number of disintegrations occurring within the source material. It's crucial to have the efficiency factor considered in calculations to obtain precise radioactivity levels.

Radioactive decay is a fundamental concept in nuclear physics, where unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. This spontaneous process leads to the transmutation of an element into another and is characterized by the decay constant, which represents the probability of a single atom decaying per unit time. The decaying process follows exponential decay laws, and the rate at which it occurs can be mathematically expressed by the activity, which is the number of disintegrations or decay events occurring per second.

Disintegration events per second is the rate at which radioactive atoms are decaying. It is synonymous with radioactivity and provides a direct measure of how 'active' a radioactive source is. This rate is crucial for quantifying the strength of a radioactive source and is directly used when expressing radioactivity in terms of Curies or becquerels. Calculating the disintegration events per second in any sample involves determining the observed counts from a detecting device, such as a Geiger counter, and adjusting for the efficiency of said device, as not every disintegration may be detected.

For calculations in physics, and specifically in radioactivity, it's essential to use consistent units. Since radioactivity is measured as disintegration events per second, time needs to be converted into seconds when calculating the number of disintegrations. Converting from minutes, hours, or days into seconds is a simple yet crucial step, involving multiplication by the number of seconds in each of those time divisions: 60 seconds in a minute, 3600 in an hour, and 86,400 in a day. Accurate conversions ensure correct computation of radioactivity and enhance the understanding of the decay process over time.