Question

Calculate the average binding energy per nucleon of 24 12Mg. Answer in units of MeV/nucleon.

Answer 1

The average binding energy per nucleon of
`^(24) _(12) Mg` is 8.00 MeV/nucleon

Step-by-step explanation:

Here we have the molar mass of
`^(24) _(12) Mg` is 23.985042 amu

The mass of a proton
`m_p` = 1.007276 amu

The mass of a neutron
`m_n` = 1.008665 amu

From the notation, 1 Mg = has 12 protons and 12 neutrons

Therefore, we find the binding energy as follows;

`E_(bind)` = 12 × (1.007276) amu + 12 × (1.008665) amu - 23.985042 amu

`E_(bind)` = 24.191292 amu - 23.985042 amu = 0.20625 amu

1 amu = 931 MeV

Therefore, 0.20625 amu = 0.20625 amu × 931 MeV = 192.01875 MeV

The average binding energy per nucleon in
`^(24) _(12) Mg` which has 24 nucleons, is thus;

`E_(bind (ave))` = 192.01875 MeV ÷ 24 = 8.00078 MeV/nucleon ≈ 8.00 MeV/nucleon.