Gold-198 has a half-life of 2.69 d. What is the activity (in curies) of a 0.86 -mg sample?

Name: Problem 65, Chapter 20: General Chemistry
Uploaded: 2021-09-17T14:38:24-08:00
Duration: 1 min 37 s
Channel: David Collins
Description: Gold-198 has a half-life of 2.69 d. What is the activity (in curies) of a 0.86 -mg sample?

step 1 To calculate the activity or the rate, in Curies, we need to know the rate equation. Rate or act

Gold-198 has a half-life of 2.69 d. What is the activity...

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This spontaneous transformation occurs at a rate characterized by probabilistic laws, leading to the conversion of one element or isotope into another over time.

Half-Life

The half-life of a radioactive substance is the time required for half of the initial number of radioactive nuclei to decay. It is a critical concept that quantifies the rate of decay without reference to the amount of substance present.

Decay Constant

The decay constant is a parameter that represents the probability per unit time that a particular nucleus will decay. It is directly related to the half-life by the relation ? = ln(2) divided by the half-life, providing a measure of the inherent decay rate of the substance.

Activity

Activity refers to the number of nuclear decays occurring per unit time in a radioactive sample. It is calculated by multiplying the decay constant by the total number of radioactive nuclei present, thereby indicating the sample’s radioactivity.

Curie

The Curie is a unit of radioactivity that standardizes the measurement of the numbers of disintegrations per second. One Curie is defined as 3.7 × 10^10 decays per second, serving as a convenient way to express large decay rates in practical situations.

Mole Concept and Avogadro's Number

The mole concept, paired with Avogadro’s number, allows for the conversion of a given mass of a substance into the number of atoms it contains. This conversion is essential in radioactivity calculations, as it provides the total number of radioactive nuclei available for decay.

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