Question

A nuclide 1 is said to be the mirror isobar of nuclide 2 if Z₁ = N₂ and Z₂ = N₁. (a) What nuclide is a mirror isobar of 11²³ Na? (b) Which nuclide out of the two mirror isobars have greater binding energy and why?

Answer 1

Mirror nuclei are nuclei where the number of protons of element one (Z₁) equals the number of neutrons of element two (N₂), the number of protons of element two (Z₂) equal the number of neutrons in element one (N₁) and the mass number is the same.

Pairs of mirror nuclei have the same spin and parity. If we constrain to an odd number of nucleons (A), then w find mirror nuclei that differ from one another by exchanging a proton with a neutron. Interesting to observe is their binding energy which is mainly due to the strong interaction and also due to Coulomb interaction. Since the strong interaction is invariant to protons and neutrons one can expect these mirror nuclei to have very similar binding energies.

(a) According to the question, nuclide 1 is said to be the mirror isobar of nuclide 2, if Z₁ = N₂ and Z₂ = N₁.

Now In ₁₁Na²³, Z₁ = 11, N₁, = 23 – 11 = 12

∴ Mirror isobar of ₁₁Na²³ is ₁₂Mg²³, for which Z₂ = 12 = N₁ and N₂ = 23 – 12 = 11 = Z₁

(b) We know 12²³Mg contains even number of protons (12) against 11²³Na which has odd number of protons (11), therefore 11²³Mg has greater binding energy than ₁₁Na²³.