Derivation of binding energy of an atom based on liquid drop model

assuming the nucleon are spherical in shape.

in the nucleus, each interior nucleon is bounded by at least 12 nucleons, each nucleon each nucleon bond has an energy U, but each bond is shared by two nucleon , the energy per nucleon will be 1/2U, and therefore in an assembly of 12 nucleons we will have 12(1/2U).

if all nucleon were at its interior the total binding energy will be

ET=6AU, where A is the atomic mass.

ET is called the volume energy.

a volume of a sphere is equal to 4πR2 =4πA2/3  if the volume energy is given by 

note we use q in place of π

SURFACE ENERGY

THE POTENTIAL ENERGY ON TO Bring protons together is

NUMBER OF PROTON PAIRS

since the  *

 *  

the coulomb energy  

THE TOTAL BINDING ENERGY

BINDING ENERGY PER NUCLEON

BUT THE NUMber of neutron exceed that of the protons , asymmetric  energy occur which can be computed as

THE PAIRING ENERGY ,  can be positive or negative

now the total energy is