Q. 5.18 - An Introduction to General, Organic, and Biological Chemistry

Question

Write a balanced nuclear equation for the positron emission of each of the following radioactive isotopes:

(a) boron-$8$

(b) ${}_8{}^{15}O$

(c) data-custom-editor="chemistry" ${}_{19}{}^{40}\mathrm{K}$

(d) nitrogen-$13$

Step-by-Step Solution

Answer

(a) The balanced equation for boron is${}_5{}^8\mathrm{B}\to {}_4{}^8\mathrm{Be}+{}_1{}^0\mathrm{e}$.

(b) The balanced equation for oxygen is${}_8{}^{15}\mathrm{O}\to {}_7{}^{15}\mathrm{N}+{}_1{}^0\mathrm{e}$ .

(c) The balanced equation of  potassium isdata-custom-editor="chemistry" ${}_{19}{}^{40}\mathrm{K}\to {}_{18}{}^{40}\mathrm{Ar}+{}_1{}^0\mathrm{e}$.

(d) The balanced equation of  nitrogen is${}_7{}^{13}\mathrm{N}\to {}_6{}^{13}\mathrm{C}+{}_1{}^0\mathrm{e}$ .

Part (a) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for positron emission.

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${}_5{}^8\mathrm{B}\to ?+{}_1{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$8=?+0$,

which states that the mass number is$8$.

By equating, find the atomic number.

which is$5=?+1$,

which states that an atomic number is$4$

So the new nucleus atom is beryllium.

Hence, the equation is${}_5{}^8\mathrm{B}\to {}_4{}^8\mathrm{Be}+{}_1{}^0\mathrm{e}$

Part (b) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for positron emission.

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${}_8{}^{15}\mathrm{O}\to ?+{}_1{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$15=?+0$,

which states that the mass number is$15$.

By equating, find the atomic number,

which is$8=?+1$,

which states that an atomic number is$7$.

So the new nucleus atom is nitrogen.

Hence, the equation is ${}_8{}^{15}\mathrm{O}\to {}_7{}^{15}\mathrm{N}+{}_1{}^0\mathrm{e}$

Part (c) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for positron emission.

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${}_{19}{}^{40}\mathrm{K}\to ?+{}_1{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$40=?+0$,

which states that the mass number is$40$.

By equating, find the atomic number,

which is$19=?+1$,

which states that an atomic number is$18$

So the new nucleus atom is argon .

Hence, the equation is ${}_{19}{}^{40}\mathrm{K}\to {}_{18}{}^{40}\mathrm{Ar}+{}_1{}^0\mathrm{e}$.

Part (d) Step 1: Given Information

We are given the isotope and we have to find the balanced nuclear reaction for positron emission.

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${}_7{}^{13}\mathrm{N}\to ?+{}_1{}^0\mathrm{e}$,

To complete it, find the mass number,

which is$13=?+0$,

which states that the mass number is$13$ .

By equating, find the atomic number.

which is$7=?+1$,

which states that an atomic number is$6$.

So the new nucleus atom is carbon.

Hence, the equation is${}_7{}^{13}\mathrm{N}\to {}_6{}^{13}\mathrm{C}+{}_1{}^0\mathrm{e}$.