(II) The activity of a sample of 35 S(T(1)/(2)=7.55 ×10^6 s) is 2.65 ×10^5 decays per second. Wh

step 1 All right, my dear student, so the formula which we will use to solve this problem is activity i

(II) The activity of a sample of 35 S(T(1)/(2)=7.55 ×10^6 s)...

Key Concepts

Radioactive Decay

Radioactive decay is a spontaneous process in which unstable atomic nuclei lose energy by emitting radiation. This process follows statistical laws and results in the transformation of the original nucleus into a different nucleus. Understanding radioactive decay is crucial when determining the amount of a radioactive substance based on measurements like activity.

Half-Life and Decay Constant

The half-life of a radioactive substance is the time required for half of the original nuclei to decay. The decay constant, which represents the probability per unit time that a single nucleus decays, is directly related to the half-life by the equation ? = ln(2)/T?/?. This relationship is essential for relating the measured activity of a sample to the number of radioactive atoms present.

Activity

Activity describes the rate at which a sample of radioactive material decays, usually measured in decays per second (Becquerels). It is calculated as the product of the decay constant and the number of radioactive atoms present. Knowing the activity helps in determining the total number of radioactive nuclei in the sample, which is an important step in further quantification such as mass determination.

Molar Mass and Avogadro’s Number

Once the number of radioactive nuclei is determined from the activity and decay constant, converting this number into a mass requires the use of Avogadro's number and the molar mass of the element. Avogadro’s number provides the number of atoms in one mole of a substance, and the molar mass converts the mole quantity into mass, thus linking nuclear decay measurements to tangible physical quantities such as the sample’s mass.

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