Question

Two nuclei having the same mass number are known as isobars. What is the difference in binding energy per nucleon for the isobars 23 11Na and 23 12Mg? The mass of 23 11Na is 22.9898 u, the mass of 23 12Mg is 22.9941 u, the mass of a proton is 1.00783 u, and the mass of a neutron is 1.00867 u, where u = 931.5 MeV/u.

Answer 1

0.21MeV

Step-by-step explanation:

For isobar 2311Na:

Actual mass of 2311Na = 22.9898u

Number of protons = 11

Number of neutrons = 23-11 = 12

Mass of 11 protons = 11 x 1.00783u = 11.08613u

Mass of 12 neutrons = 12 x 1.00867u = 12.10404u

Theoretical ( calculated) mass of 2311Na = 11.08613 + 12.10404 = 23.19017u

Mass defect, ∆m, of 2311Na = Theoretical mass – Actual mass = 23.19017 – 22.9898 = 0.20037u

Nuclear binding energy of 2311Na = ∆m x 931.5 = 0.20037u x 931.5MeV/u = 186.64MeV.

Nuclear binding energy per nucleon = Nuclear binding energy/number of nucleons = 186.64/23 = 8.11MeV.

For isobar 2312Mg:

Actual mass of 2312Mg = 22.9941u

Number of protons = 12

Number of neutrons = 23-12 = 11

Mass of 12 protons = 12 x 1.00783u = 12.09396u

Mass of 11 neutrons = 11 x 1.00867u = 11.09537u

Theoretical ( calculated) mass of 2312Mg = 12.09396 + 11.09537 = 23.18933u

Mass defect, ∆m, of 2312Mg = Theoretical mass – Actual mass = 23.18933 – 22.9941 = 0.19523u

Nuclear binding energy of 2312Mg = ∆m x 931.5 = 0.19523u x 931.5MeV/u = 181.86MeV.

Nuclear binding energy per nucleon = Nuclear binding energy/number of nucleons = 181.86/23 = 7.90MeV.

Therefore, difference in the nuclear binding energy per nucleon between 2311Na and 2312Mg = 8.11-7.90 = 0.21MeV.