Question

Write balanced equations for each of the following processes.

a. Chromium-51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture.

b. Iodine-131, used to treat hyperactive thyroid glands, decays by producing a particle.

c. Phosphorus-32, which accumulates in the liver, decays by $\mathrm{\beta }$-particle production.

Short answer

$$\begin{gathered} \mathrm{a}.{}_{24}{}^{51}\mathrm{Cr}+{}_{-1}{}^0\mathrm{e}\to {}_{23}{}^{51}\mathrm{V} \\ \mathrm{b}.{}_{53}{}^{131}\mathrm{I}\to {}_{-1}{}^0\mathrm{e}+{}_{54}{}^{131}\mathrm{Xe} \\ \mathrm{c}.{}_{15}{}^{32}\mathrm{P}\to {}_{-1}{}^0\mathrm{e}+{}_{16}{}^{32}\mathrm{S} \end{gathered}$$

Step-by-step solution

Balanced equation for the data given in (a)

The given information says that Chromium-51, which targets the spleen is used as a tracer in the studies of the red blood cells and decays by an electron capture.

Using the data, we can conclude that the mass number will remain the same. And atomic number of the product will come down by 1. Thus, the equation will be:

${}_{24}{}^{51}\mathrm{Cr}+{}_{-1}{}^0\mathrm{e}\to {}_{23}{}^{51}\mathrm{V}$

Balanced equation for the data given in (b) 

The given information says that Iodine-131 is used to treat hyperactive thyroid glands and decays by producing a beta particle.

Using the data, we can conclude that the mass number will remain the same. There is an addition of a proton, so the mass number increases by 1. Thus, the equation will be:

${}_{53}{}^{131}\mathrm{I}\to {}_{-1}{}^0\mathrm{e}+{}_{54}{}^{131}\mathrm{Xe}$

Balanced equation for the data given in (c)

The given information says that Phosphorus-32, which accumulates in a liver,

decays by a beta-particle production.

Using the data, we can conclude that the mass number will remain the same. There is an addition of a proton, so the mass number increases by 1. Thus, the equation will be:

${}_{15}{}^{32}\mathrm{P}\to {}_{-1}{}^0\mathrm{e}+{}_{16}{}^{32}\mathrm{S}$