Question

What is mirror isobars?
$(a)$ Atoms with same mass numbers but different atomic numbers
$(b)$ Two atoms with same mass numbers but different atomic numbers such that the number of protons and neutrons are interchanged.
$(c)$ Atoms with same atomic number but different mass number
$(d)$ Atoms with different numbers of protons but different number of neutrons

Answer 1

Hint: In this question think about the elements that have the same mass number but different atomic numbers such that the number of the protons and the neutrons are interchanged. Any element can be written as ${}_Z{X^A}$ where z is the atomic number and A is the atomic mass of the compound. This will help approach the solution to this problem.

Complete step-by-step solution -
Isobars
Isobars are those which have the same mass number but different protons and neutrons.
I.e. different atomic numbers but same mass number.
For example: Sulphur (S), Chlorine (Cl), Argon (Ar), Potassium (K) and Calcium (Ca) etc.
These all have the same mass number i.e. 40 but different atomic numbers.

Mirror isobars
On the other hand mirror isobars are those such as two with the same mass number but different atomic numbers such that the number of the protons and the neutrons are interchanged.
For example: ${}_{12}N{a^{23}}$and ${}_{11}M{g^{23}}$
The mass number of the sodium (Na) is 23, whereas magnesium (Mg) also has mass number 23.
It is often denoted by A.
$ \Rightarrow {A_1} = {A_2} = 23$
And the number of protons in the sodium is 12 whereas in magnesium it is 11, it is often denoted by Z.
$ \Rightarrow {Z_1} = 12{\text{ and }}{Z_2} = 11$
Now as we all know that the number of neutrons is the difference of the mass number and the number of protons, it is often denoted by N.
So number of neutrons in sodium is ${N_1} = {A_1} - {Z_1} = 23 - 12 = 11$
And number of neutrons in magnesium is ${N_2} = {A_2} - {Z_2} = 23 - 11 = 12$
So as we see that ${Z_1} = {N_2}{\text{ and }}{Z_2} = {N_1}$
So according to definition of the mirror isobars ${}_{12}N{a^{23}}$and ${}_{11}M{g^{23}}$ are called mirror isobars if${Z_1} = {N_2}{\text{ and }}{Z_2} = {N_1}$.
So as we see this is satisfied so ${}_{12}N{a^{23}}$and ${}_{11}M{g^{23}}$ are called as mirror isobars.
So this is the required answer.

Hence option (B) is the correct answer.

Note: Some examples of isobars are $^{40}S{,^{40}}Cl{,^{40}}Ar$ etc. As we can clearly see that the mass number of all three are the same but however the atomic number differs for all of them. There is another important term associated that is isotopes, it is defined as the elements that have the same atomic number but however different atomic masses.