Radon gas (Rn) is produced by the αdecay of radium 88^226 Ra. (a) How many neutrons and how man

step 1 So in this question, it's given to us that radon 222 is produced by alpha decay of radium 226. S

Radon gas (Rn) is produced by the αdecay of radium 88^226...

Radon gas $(\mathrm{Rn})$ is produced by the $\alpha$ decay of radium ${ }_{88}^{226} \mathrm{Ra}$. (a) How many neutrons and how many protons are present in the nucleus of the isotope of $\mathrm{Rn}$ produced by this decay? (b) In the air in an average size room in a student basement apartment in Ithaca, NY, there are about $10^{7}$ Rn nuclei. The Rn nucleus itself is radioactive; it too decays by emitting an $\alpha$ particle. The half-life of Rn is $3.8$ days. How many $\alpha$ particles per second are emitted by decaying Rn nuclei in the room?

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Key Concepts

Activity Calculation

Activity in nuclear physics is a measure of the decay rate of a radioactive sample and is typically expressed in decays (or disintegrations) per second. It is calculated by using the decay constant, which is derived from the half-life, and multiplying it by the total number of radioactive nuclei present.

Half-Life

The half-life of a radioactive isotope is the time required for half of a given number of nuclei to decay. It is a fundamental concept in nuclear physics used to describe the rate of decay and determines how quickly a radioactive substance diminishes over time.

Alpha Decay

Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle, consisting of two protons and two neutrons. This emission decreases the atomic number by two and the mass number by four, and is a key mechanism in the transformation of elements during radioactive decay.

Atomic Structure

This concept refers to the composition of atomic nuclei in terms of protons and neutrons. Understanding the atomic structure, including atomic number (number of protons) and mass number (total protons plus neutrons), is essential when deducing changes in a nucleus following a nuclear reaction or decay process.

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