Chapter 10, Problem 10.3E

(a)

Interpretation Introduction

Interpretation:

The number of Radon-222 nuclei decays per minute has to be given.

Concept Introduction:

In a unimolecular chemical reaction, the rate law for nuclear decay is first order.  That is, the relation between the rate of decay and the number N of radioactive nuclei present is given by the law of radioactive decay.

  $\text{Activity=k×N}$

Where, k is the decay constant.

N is the number of radioactive nuclei decay.

(b)

Interpretation Introduction

Interpretation:

The number of radioactive nuclei decay has to be given.

Concept Introduction:

Theradioactive lawstates that the probability per unit time that a nucleus will decay is a constant independent of time. This constant is calledthe decay constant and is denoted by $\text{k}$.  This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. The radioactive decay of certain number of atoms (mass) is exponential in time.

Radioactive decay law,

  ${\text{N = N}}_{\text{0}}{\text{.e}}^{\text{-kt}}$

Where N is the number of radioactive nuclei remaining after time t.

N₀ is the number of radioactive nuclei in initial time.

k is the decay constant.

t is the time required to decay.