Q. 5.17 - An Introduction to General, Organic, and Biological Chemistry

Question

Write a balanced equation for the beta decay of each of the following radioactive isotopes:

(a) silicon-$26$

(b) cobalt-$54$

(c)data-custom-editor="chemistry" ${}_{37}{}^{77}\mathrm{Rb}$

(d)data-custom-editor="chemistry" ${}_{45}{}^{93}\mathrm{Rh}$

Step-by-Step Solution

Answer

(a) The balanced equation for silicon is ${}_{14}{}^{26}\mathrm{Si}\to {}_{15}{}^{26}\mathrm{P}+{}_{-1}{}^0\mathrm{e}$.

(b) The balanced equation for cobalt is ${}_{27}{}^{54}\mathrm{Co}\to {}_{28}{}^{54}\mathrm{Ni}+{}_{-1}{}^0\mathrm{e}$.

(c) The balanced equation of rubidium is ${}_{37}{}^{77}\mathrm{Rb}\to {}_{39}{}^{77}\mathrm{Sr}+{}_{-1}{}^0\mathrm{e}$ .

(d) The balanced equation of ruthenium is ${}_{45}{}^{93}\mathrm{Rh}\to {}_{46}{}^{93}\mathrm{Pa}+{}_{-1}{}^0\mathrm{e}$ .

Part (a) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for beta decay.

Part (a) Step 2: Explanation

To find out the balanced nuclear equation, we need to find out the mass number and atomic number of the new nucleus atom.

In the beginning, the equation is${}_{14}{}^{26}\mathrm{Si}\to ?+{}_{-1}{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$26=?+0$,

which states that the mass number is$26$.

By equating, find the atomic number.

which is$14=?-1$,

which states that an atomic number is$15$

So the new nucleus atom is phosphorous.

Hence, the equation is  ${}_{14}{}^{26}\mathrm{Si}\to {}_{15}{}^{26}\mathrm{P}+{}_{-1}{}^0\mathrm{e}$

Part (b) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for beta decay.

Part (b) Step 2: Explanation

To find out the balanced nuclear equation, we need to find out the mass number and atomic number of the new nucleus atom.

In the beginning, the equation is${}_{27}{}^{54}\mathrm{Co}\to ?+{}_{-1}{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$54=?+0$,

which states that the mass number is$54$.

By equating, find the atomic number,

which is$27=?-1$,

which states that an atomic number is$28$.

So the new nucleus atom is nickel.

Hence, the equation is ${}_{27}{}^{54}\mathrm{Co}\to {}_{28}{}^{54}\mathrm{Ni}+{}_{-1}{}^0\mathrm{e}$

Part (c) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for beta decay.

Part (c) Step 2: Explanation

To find out the balanced nuclear equation, we need to find out the mass number and atomic number of the new nucleus atom.

In the beginning, the equation is${}_{37}{}^{77}\mathrm{Rb}\to ?+{}_{-1}{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$77=?+0$,

which states that the mass number is$77$.

By equating, find the atomic number,

which is$37=?-1$,

which states that an atomic number is$38$

So the new nucleus atom is strontium.

Hence, the equation is ${}_{37}{}^{77}\mathrm{Rb}\to {}_{39}{}^{77}\mathrm{Sr}+{}_{-1}{}^0\mathrm{e}$.

Part (d) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for beta decay.

Part (d) Step 2: Explanation

To find out the balanced nuclear equation, we need to find out the mass number and atomic number of the new nucleus atom.

In the beginning, the equation is${}_{45}{}^{93}\mathrm{Rh}\to ?+{}_{-1}{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$93=?+0$,

which states that the mass number is$93$ .

By equating, find the atomic number.

which is$45=?-1$,

which states that an atomic number is$46$.

So the new nucleus atom is palladium.

Hence, the equation is ${}_{45}{}^{93}\mathrm{Rh}\to {}_{46}{}^{93}\mathrm{Pa}+{}_{-1}{}^0\mathrm{e}$.