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Journal of Radioanalytical Chemistry

, Volume 10, Issue 1, pp 105–116 | Cite as

The influence of statistical error in radioactivity counting on the precision of isotope dilution analysis, I

  • M. Kyrš
  • Miss T. Vrana
Physical Methods Section

Abstract

The influence of the statistical error in measuring radioactive samples in direct isotope dilution analysis is analytically studied for several practically important sets of conditions. Formulas are given to calculate the optimum amount of radioactive substance to be added in order to minimize the error involved. Both cases with negligible background count rates and cases where the background must be considered are treated. In some cases recommendations are given for the times of measurement of background, undiluted and diluted sample.

Keywords

Count Rate Statistical Error Dilute Sample Percentage Yield Radioactive Substance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Symbols

b

background count rate

p

proportionality constant relatingR toSW

t0

time of measurement of the undiluted sample

tB

time of measurement of background

t2

time of measurement of the diluted sample

R

count rate corrected for background (R=R t−b)

Rt

count rate including background

S0

specific activity of the undiluted radioactive sample

S2

specific activity after dilution

W0

weight of radioactive substance added in the dilution step

W′

weight of substance isolated ‘substoichiometrically’ (W′=W 1=Wis 2)

W1

weight of the substance in determiningS 0

Wis2

weight of the substance in determiningS 2

Wx

unknown weight of element to be determined in the sample

δ

relative standard error ofS 0 (δ=ΔS 0/S 0)

ε

relative standard error ofW x (ε=ΔW x/Wx)

ϕ

W 0/Wx

τ

total time of measurement (τ=t B +t0+t2)

\(\bar \tau \)

t B +t2

w

\({{t_2 } \mathord{\left/ {\vphantom {{t_2 } {\bar \tau }}} \right. \kern-\nulldelimiterspace} {\bar \tau }}\)

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References

  1. 1.
    B. S. Coulter,Intern. J. Appl. Radiation Isotopes, 20 (1969) 271.CrossRefGoogle Scholar
  2. 2.
    T. Braun, J. Tölgyessy, M. Kyrš, Isotope Dilution Analysis, Pergamon, Oxford, 1971.Google Scholar
  3. 3.
    K. Schmeiser, Radionuclides, Springer, Berlin, 1963.Google Scholar
  4. 4.
    J. Růžička, J. Starý, Substoichiometry in Radiochemical Analysis, Pergamon, Oxford, 1967.Google Scholar

Copyright information

© Akadémiai Kiadó 1972

Authors and Affiliations

  • M. Kyrš
    • 1
  • Miss T. Vrana
    • 1
  1. 1.Engineering Faculty of Middle East Technical UniversityAnkara(Turkey)

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