Chapter 25, Problem 26PS

Interpretation Introduction

Interpretation:

The equation is to be written for the radioactive decay series Thorium-232 to Pb-207.

Concept introduction:

In this radioactive decay process the unstable isotopes loses their energy by emitting radiation. It is converted in to stable isotopes. The emitting radiations are Alpha emission and Beta emission.

β − decay (electron emission): ${}_{\text{-1}}^{\text{0}}\text{β}$

α − decay (Helium nuclei emission): ${}_{\text{2}}^{\text{4}}\text{He}$

Explanation of Solution

The radioactive decay series beginning with Th-232 and ending with Pb-208 is as follows.

$\left(\begin{array}{l}Thorium-232\stackrel{\alpha }{\to }Radium-228\stackrel{\beta }{\to }Actinium-228\stackrel{\beta }{\to }Thorium-228\\ \alpha \downarrow \\ lead-212\stackrel{\alpha }{\leftarrow }polonium-216\stackrel{\alpha }{\leftarrow }Radon-220\stackrel{\alpha }{\leftarrow }Radium-224\\ \beta \downarrow \end{array}\right)$

$\left(\begin{array}{l}Bismuth-212\\ \downarrow \beta \\ Polonium-212\underset{\alpha }{\leftarrow }Lead-208\end{array}\right)$

The equations for each step occurring in the following sequence:

$\alpha ,\beta ,\beta ,\alpha ,\alpha ,\alpha ,\alpha ,\beta ,\beta ,\alpha$.

The radioactive isotope of Thorium-232 is transmitted to Radium-228 by emission of Alpha particle.

$Th\stackrel{\alpha }{\to }Ra$

The radioactive isotope of Radium-228 is transmitted to Actinium-228 by the emission of Beta particle.

$Ra\stackrel{\beta }{\to }Ac$

The radioactive isotope of Actinium-228 is transmitted to Thorium-228 by the emission of Beta particle.

$Ac\stackrel{\beta }{\to }Th$

The radioactive isotope of Thorium-228 is transmitted to Radium-228 by the emission of Alpha particle.

$Th\stackrel{\alpha }{\to }Ra$

The radioactive isotope of Radium-228 is transmitted to Radon-220 by the emission of Alpha particle.

$Ra\stackrel{\alpha }{\to }Rn$

The radioactive isotope of Radon-220 is transmitted to Polonium-216 the emission of Alpha particle.

$Rn\stackrel{\alpha }{\to }Po$

The radioactive isotope of Polonium-216 is transmitted to Lead-212 by the emission of Alpha particle.

$Po\stackrel{\alpha }{\to }Pb$

The radioactive isotope of Lead-212 is transmitted to Bismuth-212 by the emission of Beta particle.

$Pb\stackrel{\beta }{\to }Bi$

The radioactive isotope of Bismuth-212 is transmitted to Thallium-208 by the emission of Beta particle.

$Bi\stackrel{\beta }{\to }Po$

The radioactive isotope of Polonium-212 is transmitted to Lead-207 by the emission of Alpha particle.

$Po\stackrel{\alpha }{\to }pb$

Conclusion

The equation was written for the radioactive decay series Thorium-232 to Pb-207.