To calculate the binding energy per nucleon of 20 Ca40, we need to find the total binding energy and divide it by the total number of nucleons in the nucleus.
Step 1: Find the total binding energy.
The total binding energy can be calculated using the formula:
Binding energy (in MeV) = (Atomic mass of the nucleus - Sum of the masses of its individual protons and neutrons) * 931 MeV
The atomic mass of 20 Ca40 is given as 39.975 a.m.u. Given that 1 a.m.u is equal to 931 MeV, we need to convert the atomic mass to MeV:
Atomic mass (in MeV) = 39.975 a.m.u * 931 MeV/a.m.u
Step 2: Find the number of nucleons.
Since 20 Ca40 has 20 protons (given by the atomic number) and 20 neutrons, the total number of nucleons can be calculated as:
Number of nucleons = Number of protons + Number of neutrons = 20 + 20
Step 3: Calculate the binding energy per nucleon.
Finally, the binding energy per nucleon can be found by dividing the total binding energy by the total number of nucleons:
Binding energy per nucleon = Total binding energy / Number of nucleons
Let's calculate the values:
Step 1: Calculate the atomic mass in MeV:
Atomic mass (in MeV) = 39.975 a.m.u * 931 MeV/a.m.u = 37,263.525 MeV
Step 2: Calculate the number of nucleons:
Number of nucleons = 20 protons + 20 neutrons = 40 nucleons
Step 3: Calculate the binding energy per nucleon:
Binding energy per nucleon = 37,263.525 MeV / 40 nucleons
Therefore, the binding energy per nucleon of 20 Ca40 is approximately 931.59 MeV.