If the mass of proton=1.008 a.m.u. and mass of neutron=1.009 a.m.u., then binding energy per nucleon for Be₄₉ (mass=9.012 amu) would be:

• A. 40.065 Mev
• B. 60.44 Mev
• C. 67.2 Mev
• D. 6.72 Mev

To find the binding energy per nucleon for the beryllium isotope Be₄₉, we first need to calculate the mass defect and then convert that into binding energy. Here’s how to do it step by step:

Step 1: Calculate the Total Mass of Nucleons

Beryllium-9 has 4 protons and 5 neutrons. The total mass of the nucleons can be calculated as follows:

• Mass of protons = 4 protons × 1.008 a.m.u. = 4.032 a.m.u.
• Mass of neutrons = 5 neutrons × 1.009 a.m.u. = 5.045 a.m.u.

Total mass of nucleons = 4.032 a.m.u. + 5.045 a.m.u. = 9.077 a.m.u.

Step 2: Calculate the Mass Defect

The mass defect is the difference between the total mass of the nucleons and the actual mass of the nucleus:

Mass defect = Total mass of nucleons - Actual mass of Be₄₉

Mass defect = 9.077 a.m.u. - 9.012 a.m.u. = 0.065 a.m.u.

Step 3: Convert Mass Defect to Energy

Using Einstein's equation \(E = mc^2\), we convert the mass defect to energy. The conversion factor is approximately 931.5 MeV/c² per a.m.u:

Binding energy = Mass defect × 931.5 MeV/a.m.u.

Binding energy = 0.065 a.m.u. × 931.5 MeV/a.m.u. ≈ 60.44 MeV.

Step 4: Calculate Binding Energy per Nucleon

To find the binding energy per nucleon, divide the total binding energy by the number of nucleons (9 for Be₄₉):

Binding energy per nucleon = Total binding energy / Number of nucleons

Binding energy per nucleon = 60.44 MeV / 9 ≈ 6.72 MeV.

Final Answer

The binding energy per nucleon for Be₄₉ is 6.72 MeV. Therefore, the correct option is D. 6.72 MeV.