The activity of a sample containing carbon-14 is \(54.8 \mathrm{~Bq}\). Express this activity in microcuries.

When discussing radioactivity, the unit 'Becquerel' is essential. Named after the French physicist Henri Becquerel, who discovered radioactivity, a Becquerel represents the activity of a quantity of radioactive material in which one nucleus decays per second. The formal definition is:

The SI unit of radioactive decay defined as one disintegration per second. It provides a measure of the rate at which a certain amount of radioactive substance undergoes transmutation. To put it simply, if you have a sample of a radioactive element and it has an activity of 1 Bq, this means that one atom in the sample undergoes radioactive decay each second. This unit helps scientists and healthcare professionals assess the potential hazards of radioactive materials and design safety protocols accordingly.

Understanding this unit is crucial when quantifying the activity of radioisotopes like carbon-14, especially in fields such as nuclear medicine, radiocarbon dating, and environmental monitoring.

The Curie, abbreviated as Ci, is another unit that measures radioactivity. It's named in honor of the pioneering scientists Marie and Pierre Curie, who conducted groundbreaking work in the field of radioactivity. Unlike the Becquerel which is the standard International System of Units (SI) measurement, the Curie is an older, non-SI unit that is still widely used in the United States.

Curie (Ci):

The unit of radioactivity that corresponds to the disintegration of 3.7 x 10^10 atomic nuclei per second. This value was originally defined based on the activity of one gram of radium-226. Since the Becquerel represents a much smaller quantity, the Curie is generally used for describing activities of larger samples where a high number of disintegrations occur every second. The Curie facilitates easier communication and understanding in practical applications like medical treatments, where radioactive sources of significant activity are common.

Carbon-14 is a radioisotope of carbon that is naturally occurring and is continually being formed in the upper atmosphere when cosmic rays interact with nitrogen atoms. With a half-life of about 5,730 years, carbon-14 decays by emitting beta particles and transforming into nitrogen-14, which is a process scientists can measure. This property of carbon-14 makes it incredibly valuable in a dating technique known as radiocarbon dating, which is used to determine the age of carbon-containing materials up to about 60,000 years old.

Radioisotope Carbon-14:

A radioactive version of carbon with an atomic mass number of 14 used especially in tracing metabolic pathways and in radiocarbon dating archaeological findings. It's activity, measured in either Becquerel or Curie, signifies the rate at which the carbon-14 atoms are decaying in a given sample. Due to its predictable decay rate, the presence and activity level of carbon-14 in organic materials help archaeologists and geologists determine the chronological age of ancient objects and environmental samples.

When dealing with radioactive materials, it's often necessary to convert between different units of activity. This is because certain regions, industries, or scientific disciplines may prefer one unit over another. The step-by-step solution provided in the exercise outlines how to convert activity measurements from becquerels to microcuries. Understanding this process requires familiarity with basic conversion factors and operations.

When converting, we employ the knowledge that 1 Ci equals 3.7 x 10^10 Bq, which is a reflection of the Curie being much larger than the Becquerel. To adjust for scale, the conversion involves dividing the activity in Bq by this factor to translate it into Curies. Next, since the exercise asks for microcuries, we must remember that there are 10^6 (1,000,000) microcuries in a single Curie. Consequently, after finding the activity in Curies, it is multiplied by this number. Having proficiency in these conversions is imperative for scientists working with isotopic labels, medical professionals using radioactive treatments, and safety regulators monitoring radiation exposure levels.