Q.4. Calculate the binding energy per nucleon of 20 Ca40 which has atomic mass of 39.975 a.m.u The mass of
hydrogen atom is 1.0078 a.m.u and that of neutron is 1.0086 a.m.u (1 a.m.u = 931 Mev) (10)
20 neutrons and 20 protons (with electrons) separately would have a mass of 40.328 amu
As a Ca atom with electrons, the mass is 39.975 amu
The mass difference (binding energy) of 0.353 amu (after converting to kg) can be converted to Joules using
E = m c^2, OR
if you want it in Mev, just multiply by 931 Mev/amu
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.