Question

A sample giving \(3.7 \times 10^{10}\) disintegrations per second has what activity in \(\mathrm{Ci}\) and in \(\mathrm{Bq}\) ?

Short answer

The activity is \(3.7 \times 10^{10}\) Bq and approximately 1 Ci.

Step-by-step solution

Convert to Becquerel

The activity in becquerels can be found directly from the disintegration rate given, as 1 becquerel (Bq) is equivalent to 1 disintegration per second. Therefore, to convert the disintegration rate to Bq, you simply use the same numerical value but change the unit.

Convert to Curie

To convert the activity to curies (Ci), use the conversion factor where 1 Ci equals to \(3.7 \times 10^{10}\) Bq. Divide the given disintegration rate by the conversion factor to obtain the activity in curies.

Key concepts

Becquerel (Bq)

Understanding the Becquerel is fundamental when studying nuclear chemistry. The Becquerel, named after physicist Henri Becquerel, is the SI unit of radioactivity. It is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. A simple way to visualize this is to imagine a single atom undergoing radioactive decay every second.

When you are given a disintegration rate, like in the exercise where a sample's activity is given as \(3.7 \times 10^{10}\) disintegrations per second, this unit directly translates into the same number of Becquerels. Thus, an activity of \(3.7 \times 10^{10}\) disintegrations per second is simply \(3.7 \times 10^{10}\) Bq. This one-to-one correspondence makes the concept straightforward for students to grasp.

Curie (Ci)

The Curie (Ci) is another unit used to measure radioactive decay, where 1 Ci is historically based on the activity of 1 gram of radium-226. In modern terms, it is defined as \(3.7 \times 10^{10}\) disintegrations per second. This large number is a reflection of the significant amount of activity in a relatively small amount of radioactive substance.

To convert from Becquerels to Curies, you utilize the conversion factor as seen in the provided exercise. If an activity is \(3.7 \times 10^{10}\) Bq, since 1 Ci equals \(3.7 \times 10^{10}\) Bq, the activity is also 1 Ci. The conversion factor simplifies many calculations and is a crucial constant for those studying nuclear chemistry.

Nuclear Chemistry

Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, and transformations in the nuclei of atoms. It encompasses the study of the chemical effects resulting from the absorption of radiation within living animals, plants, and other materials.

Radioactive decay is a core concept within this field and refers to the process by which an unstable atomic nucleus loses energy by emitting radiation. Understanding the rate at which this process occurs - the disintegration rate - is essential for many applications, including medical diagnosis and treatment, determining the age of artifacts, and handling nuclear power.

Disintegration Rate

The disintegration rate, often measured in disintegrations per second, describes how quickly unstable nuclei are decaying within a sample. In practice, it's a way of quantifying the level of radioactivity of a substance. The faster the disintegration rate, the more radioactive the sample is.

As seen in the exercise, the given sample has a disintegration rate of \(3.7 \times 10^{10}\) per second. To effectively convey its level of activity, it can be labeled with the units of Bq or Ci. In essence, this metric grants a clear perspective on the sample's radioactivity, allowing us to determine potential uses or risks associated with its handling.