A by-product of some fission reactors is the isotope ^23994 Pu which is an alpha emitter with a

step 1 Okay, today I'm going to explain this question. So for this one, we have something we need to kn

A by-product of some fission reactors is the isotope ^23994...

A by-product of some fission reactors is the isotope $^{239}_{94} \mathrm{Pu}$ which is an alpha emitter with a half-life of 24,000 years: $$_{94}^{239} \mathrm{Pu} \longrightarrow_{92}^{235} \mathrm{U}+\alpha$$ Consider a sample of $1 \mathrm{kg}$ of pure $^{239}_{94} \mathrm{Pu}$ at $t=0$ Calculate (a) the number of $^{239}_{94}$ Pu nuclei present at $t=0,$ (b) the initial activity in the sample, and (c) the time required for the activity to decrease to 1 decay/s.

Key Concepts

Exponential Decay Law

The exponential decay law mathematically describes how the quantity of radioactive nuclei in a sample decreases over time. It uses the decay constant and the initial number of nuclei to model the number of remaining nuclei at any later time. This law is fundamental for predicting the behavior of radioactive substances in various applications, including the calculation of activity and the determination of decay time scales.

Avogadro's Number and Molar Mass

Avogadro's number is used to convert the mass of a substance into the number of particles (atoms or nuclei), by relating the mass of a sample to the number of atoms it contains through the substance's molar mass. This conversion is critical when quantifying the initial number of nuclei in a radioactive sample, serving as the basis for further calculations related to decay.

Activity

Activity is defined as the rate at which a sample of radioactive material decays, typically measured in decays per second (becquerels). It is proportional to the number of undecayed nuclei present and the decay constant. This concept is essential for assessing the intensity of radioactive emissions from a material over time.

Half-life and Decay Constant

The half-life of a radioactive substance is the time required for half of the nuclei in a sample to decay. It is closely related to the decay constant, which quantifies the probability per unit time that a single nucleus will decay. These concepts are foundational in determining how quickly a radioactive substance transforms and in calculating the remaining quantity of the substance at any given time.

Radioactive Decay

Radioactive decay is a stochastic (random) process by which an unstable atomic nucleus loses energy by emitting radiation. Understanding this process is crucial because it explains how a substance transforms into another over time and provides the framework for quantifying the rate of such transformation.

Transcript

Please give Ace some feedback