(II) The activity of a sample of (35)/(16) S(T(1)/(2)=87.32 days ) is 3.65 ×10^4 decays per seco

step 1 Okay, so this one's pretty similar to ones before it. You're given half -life and the activity a

(II) The activity of a sample of (35)/(16) S(T(1)/(2)=87.32...

Key Concepts

Activity

Activity refers to the number of decay events occurring per unit time in a radioactive sample and is measured in becquerels (decays per second). It quantifies how rapidly a radioactive substance is decaying, which is important for both practical applications and theoretical calculations in nuclear chemistry.

Decay Constant

The decay constant is a proportionality factor that relates the probability per unit time of a single nucleus decaying. It is mathematically related to the half-life by the equation ? = ln(2)/t½. This constant is essential for converting between the half-life and the activity of a radioactive sample.

Mass Calculation from Decay Data

Calculating the mass of a radioactive sample using its activity involves several steps: determining the decay constant, relating the activity to the number of undecayed nuclei, and then converting this number into mass using Avogadro’s number and the molar mass of the isotope. This process integrates concepts from exponential decay kinetics and stoichiometry.

Radioactive Decay

This is the process by which an unstable atomic nucleus loses energy by emitting radiation. It is a random but statistically predictable process in which atoms transform into other atoms or isotopes, releasing particles and energy with each decay event. The study of radioactive decay is central to nuclear chemistry and physics, as it helps in determining the transformations and energy outputs of various nuclear reactions.

Half-Life

The half-life of a radioactive substance is the time required for half of the initial number of radioactive nuclei to undergo decay. It is a key parameter that characterizes the rate of decay for a radioactive isotope and is useful in applications ranging from radiometric dating to nuclear medicine and energy generation.

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