(II) A sample of 49 K is decaying at a rate of 6.70 ×10^2 decays/s. What is the mass of the samp

step 1 My dear student, the formula which we will use to solve this problem is number of decays or numb

(II) A sample of 49 K is decaying at a rate of 6.70 ×10^2...

Key Concepts

Radioactive Decay Law

This concept explains how unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. The decay process is statistically random and can be described by an exponential decay law, where the number of undecayed nuclei decreases over time. The law is essential for connecting the measurable rate of decay (activity) to the total number of radioactive atoms present in a sample.

Activity of a Radioactive Sample

Activity is a measure of the number of decays per second in a radioactive sample, quantified in units such as becquerels. It reflects the sample’s instantaneous rate of nuclear transformation and is directly proportional to the number of radioactive nuclei present. The relationship A = ?N (where A is the activity, ? is the decay constant, and N is the number of nuclei) is pivotal when determining the original quantity of material from its decay rate.

Decay Constant

The decay constant (?) characterizes the probability per unit time that a nucleus will decay. It is directly related to the half?life of an isotope by the relationship ? = ln(2)/t1/2. Knowing ? is critical for connecting the observed decay rate (activity) with the number of radioactive atoms in a sample, which is later used for mass calculations.

Stoichiometry and Molar Conversions

This concept involves converting between the number of atoms, moles, and measurable quantities like mass. Using Avogadro’s number, one can convert the number of radioactive atoms derived from the decay rate and decay constant into moles. With the molar mass of the isotope, the number of moles is then converted into mass, providing the means to determine the physical mass of the radioactive sample based on its activity.

Transcript

Please give Ace some feedback