   Chapter 33, Problem 52PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider a detector needed to observe the proposed, but extremely rare, decay of an electron. Construct a problem in which you calculate the amount of matter needed in the detector to be able to observe the decay, assuming that it has a signature that is clearly identi?able. Among the things to consider are the estimated half life (long for rare events), and the number of decays per unit time that you wish to observe, as well as the number of electrons in the detector substance.

To determine

The amount of sodium - 24 in a detector in which electron decay is being observed with an activity of 200 GCi.

Explanation

Given info:

Activity =200×109 Ci =200×109×3.7×1010 Becquerel

Half life of sodium - 24 =14.9 hours

Formula used:

Activity of an isotope with N0 number of initial particles and decay constant λ is given by,

R=λN0=0.693t12N0

Where, t12 half life of the isotope

Calculation:

Initial number of electrons, N0=Rt120.693=200×109×3

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