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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?
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Solution
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.
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