   Chapter 25, Problem 48PS

Chapter
Section
Textbook Problem

Scandium occurs in nature as a single isotope, scandium-45. Neutron irradiation produces scandium-46, a β emitter with a half-life of 83.8 days. If the initial activity is 7.0 × 104 dpm, draw a graph showing disintegrations per minute as a function of time during a period of 1 year.

Interpretation Introduction

Interpretation: The graph should be drawn for disintegrations per minute as a function of time during a period of 1 year.

Concept Introduction:

Nuclear reaction is a physical process in which there is a change in identity of an atomic nucleus. Natural radioactive decays, artificial radioactive decays... are considered as nuclear reactions because these processes make changes in the identity of an atomic nucleus.

Half–life period: It is the time required for the concentration of radioactive substance to reduce to the one-half of its initial concentration.

The integrated rate law for the first order is as follows:

ln[A]=ln[A0]ktwhere,[A0]= initialconcentrationk=rate constantt=time[A]=concentrationaftertimet

Explanation

Half-life of Scandium-46 is 83.8 days.

Initial activity is 7.0 ×104dpm.

Time of period=1year.

According to integrated first order rate equation,

ln[A] = -Kt + ln[A0]

K = 0.693t1/2

K=0.69383.8days=8.27×10-3days-1

According to disintegrated first order rate equation.

ln[A] = -k(t) + ln[Ao]

Substitute the value as follows:

ln[A]=[(8

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