Question

which of the following are the examples of the mirror isobars?
A) $_1{H^1}$ and $_1{H^2}$
B) $_6{C^{12}}$ and $_6{C^{13}}$
C) $_{11}N{a^{23}}$ and $_{12}M{g^{23}}$
D) $_{11}N{a^{23}}$ and $_{12}M{g^{24}}$ .

Answer 1

Any element can be written as $_z{X^y}$ where $z$ is the atomic number and $y$ is the atomic mass. The atomic number is the number of protons in an atom of an element. Atomic mass is the sum of protons and neutrons in an atom of an element. Two elements A and B are said to be mirror isobars if the numbers of protons of elements A equals the numbers of neutrons of element B and the number of protons of element B equals the number of neutrons of element A. Therefore the mass number will be the same for mirror isobars. Some examples of mirror isobars are $N^{15}$ and $O^{15}$, ${Na}^{24}$ and ${Al}^{24}$, etc. We can find out the number of neutrons by subtracting the atomic number from the atomic mass as the atomic mass is the sum of neutrons and protons.

Complete solution:
Consider the first option. We are given $_1{H^1}$ and $_1{H^2}$ . Let us calculate the number of protons and neutrons for each element.
For $_1{H^1}$ the atomic mass is 1. Therefore the number of protons $p = 1$ and number of neutrons $n = 0$ .
For $_1{H^2}$ the atomic mass is 2. Therefore the number of protons $p = 1$ and number of neutrons $n = 2 - 1 = 1$
Here we see that the number of protons and the number of neutrons are not exchanged. Therefore these elements are not mirror isobars.
Now calculate the number of protons and electrons for $_6{C^{12}}$ and $_6{C^{13}}$ .
For $_6{C^{12}}$ the atomic mass is 12. Therefore the number of protons $p = 6$ and the number of neutrons $n = 12 - 6 = 6$
For $_6{C^{13}}$ the atomic mass is 13. Therefore the number of protons $p = 6$ and the number of neutrons $n = 13 - 6 = 7$
Here also the number of protons and neutrons are not exchanged. Therefore these elements are not mirror isobars.
Now calculate the number of protons and electrons for $_{11}N{a^{23}}$ and $_{12}M{g^{23}}$ .
For $_{11}N{a^{23}}$ the atomic mass is 23. Therefore the number of protons $p = 11$ and the number of neutrons $n = 23 - 11 = 12$ .
For $_{12}M{g^{23}}$ the atomic mass is 23. Therefore the number of protons $p = 12$ and the number of neutrons $n = 23 - 12 = 11$ .
Here we see that the number of protons and the number of neutrons are exchanged. Therefore these elements are mirror isobars.
Let us check for option D.
For $_{11}N{a^{23}}$ the atomic mass is 23. Therefore the number of protons $p = 11$ and number of neutrons $n = 23 - 11 = 12$ .
For $_{12}M{g^{23}}$ the atomic mass is 24. Therefore the number of protons $p = 12$ and the number of neutrons $n = 24 - 12 = 12$ .
The number of protons and the number of neutrons are not exchanged. Therefore these elements are not mirror isobars.

Hence the correct option is C.

Note: Whenever you are asked to tell which pair of elements are mirror isobars first you make sure that their atomic masses are equal. If the atomic masses of two elements are not equal then the elements cannot be mirror isobars. Isobars and mirror isobars are not the same. Isobars are elements having the same atomic mass while mirror isobars are the elements having the same atomic mass and number of protons and neutrons that can be exchanged.