# Half Life of Radioactive Isotope

The Half Life of a Radioisotope

By Jeremiah Stoddard

Abstract:

The half-life of a radioisotope is the time required for half the atoms in a given sample to undergo radioactive, or nuclear, decay. Half-life is given the symbol t1/2.Different radioisotopes have different half-lives. The amount of radioactive isotope remaining can be calculated using the equation, ln [ (A)0 / (A) t1/2 ] = kt1/2 , or, rearranged: ln 2 = kt1/2. A sample data set was provided due to safety concerns. Using the data set, a half-life of 14.46 days was calculated using graphical linear regression analysis.

Introduction:

Unstable isotopes of certain elements spontaneously disintegrate. Their nuclei discharge particles or energy. Observing the decay stages using an appropriate instrument allows the researcher to determine the radioactive decay rate. The decay rate can be calculated using the formula: ln [ (A)0 / (A) t1/2 ] = kt.

The half-life of the isotope was considered to be the time at which the activity has dropped to ½ its original value and was given the symbol, t1/2. Calculation of the half-life was determined with the equation ln [ (A)0 / (A) t1/2 ] = kt1/2 , or, rearranged: ln 2 = kt1/2.

Materials:

This lab was performed under theoretical conditions, as the proper facilities for studying radioactive materials were unavailable. As such, the materials consisted of a data sheet for the half-life of a radioisotope. In real world conditions, a Geiger-Mueller tube and a radioactive sample would be necessary.

Methods:

Using the provided data in Table 1, the time in days, the normalized activity of the unknown (A`), and the natural log of the normalized activity of the unknown (ln A`) was calculated to determine beta emission half-life, and the half-life of the radioisotope. This data was then plotted on a graph to determine half-life.

The calculation for A` was A`unk = At (S0/St), where:

S0 = corrected activity of standard at elapsed time =...

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