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 What is the Semi Empirical Mass Formula?

Answer:

Semi Empirical Mass Formula

V. Weizsäcker proposed an equation in terms of atomic mass of the nuclide and series of binding energy term in 1935. This equation is known as Semi Empirical Mass Formula or V. Weizsäcker formula. This equation contains five factors that contribute to the binding energy of nuclei i.e. Surface energy term, Volume energy term, Coulomb Energy term, Asymmetry energy term and Pairing energy term. The volume term, being directly proportional to the number of nucleons, illustrates the idea that each nucleon only interacts with its nearest neighbors and binds to the nucleus at a specific binding energy.

So the mass of atom is defined by: Semi Empirical Mass Formula

_ZM^A = (Z*M_p + N*M_n) – (Binding Energy in terms of mass unit)

Z = Number of protons; M_p = Mass of proton; N = Number of neutron; M_n = Mass of neutron; _ZM^A =Atomic mass of nuclide

Total Binding Energy = Surface energy term E_sa + Volume energy term E_Vol + Coulomb Energy term E_coul + Asymmetry energy term E_asy + Pairing energy term E_Pa.

_ZM^A = (Z*M_p + N*M_n) – (E_sa  + E_Vol  + E_coul + E_asy + E_Pa )

• Surface energy: A nucleon at the surface of a nucleus interacts with fewer other nucleons than one in the interior of the nucleus and hence its binding energy is less.This surface energy term takes that into account and is therefore negative and is proportional to the surface area.

E_sa = -A_s* A^2/3

A_s = Propostional constant A = total number of nucleons

•  Volume energy: When an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it. So, this nuclear energy is proportional to the volume.

E_Vol = A_v*A   ; A_v = constant.

• CoulombEnergy: The electric repulsion between each pair of protons in a nucleus contributes toward decreasing its binding energy.

E_coul = -A_cZ (Z-1) / A^1/3   ; A_c = Constant, Z = Number of protons.

• Asymmetry energy:Energy associated with the Pauli Exclusion Principle. Were it not for the Coulomb energy, the most stable form of nuclear matter would have the same number of neutrons as protons, since unequal numbers of neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type.

E_asy = -A_as (A-2Z)² / A ;       A_as = Constant.

• Pairing energy: An energy which is a correction term that arises from the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number.

So the Semi Empirical mass formula is

_ZM^A = (Z*M_p + N*M_n) – (-A_s* A^2/3 + A_v*A -A_cZ (Z-1) / A^1/3 – A_as (A-2Z)² / A + E_pa)

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