Binding Energy


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An Overview : 

An Overview Atomic mass unit Mass-energy equivalence Mass defect Binding energy Packing fraction BE Curve

Atomic mass number : 

Atomic mass number The chemist John Dalton was the first to suggest the mass of one atom of hydrogen as the atomic mass unit. Francis Aston, inventor of the mass spectrometer, later used 1⁄16 of the mass of one atom of oxygen-16 as his unit.

Slide 4: 

1 u = 1/NA gram = 1/ (1000 NA) kg  (where NA is Avogadro's number) 1 u = 1.660538782(83)×10−27 kg = 931.494027(23) MeV/c2 The precise definition is that it is one twelfth of the mass of an unbound atom of carbon-12 (12C) at rest and in its ground state.

Mass energy equivalence : 

Mass energy equivalence In physics, mass–energy equivalence is the concept that any mass has an associated energy and vice versa. In special relativity this relationship is expressed using the mass–energy equivalence formula E = mc^2 where E = energy, m = mass, c = the speed of light in a vacuum , The formula was derived by Albert Einstein, who arrived at it in 1905 Einstein was the first to propose that the equivalence of mass and energy is a general principle, a consequence of the symmetries of space and time. In the formula, c2 is the conversion factor required to convert from units of mass to units of energy . In unit-specific terms, E (in joules) = m (in kilograms) multiplied by (299,792,458 m/s)2.

Mass defect : 

Mass defect An atom of carbon 12 is made of six protons, six neutrons, and six electrons, which when added together have a mass of 12.095646 amu. But carbon 12 is defined as having an atomic weight of exactly 12.000000 — in fact this is the standard by which all other atomic weights are defined. This mass discrepancy is called the Mass Defect, and is one of the fundamental properties of nuclear physics. This mass discrepancy is called the mass defect, and is one of the fundamental properties of nuclear physics. When nucleons come together to form an atomic nucleus, a fraction of their mass is lost as it is converted to energy and released as electromagnetic radiation.

Slide 7: 

Mass Defect :

Binding energy : 

Binding energy Binding energy represents the mechanical work which must be done in acting against the forces which hold an object together, while disassembling the object into component parts separated by sufficient distance that further separation requires negligible additional work.

Types of binding energy : 

Types of binding energy Electron binding energy is a measure of the energy required to free electrons from their atomic orbits. Nuclear binding energy is derived from the strong nuclear force and is the energy required to disassemble a nucleus into free unbound neutrons and protons, strictly so that the relative distances of the particles from each other are infinite At the atomic level, the atomic binding energy of the atom derives from electromagnetic interaction and is the energy required to disassemble an atom into free electrons and a nucleus. In astrophysics, gravitational binding energy of a celestial body is the energy required to disassemble it into space debris . This quantity is not to be confused with the gravitational potential energy, which is the energy required to separate two bodies, such as a celestial body and a satellite, to infinite distance, keeping each intact .

Packing fraction : 

Packing fraction Atomic packing factor (APF) or packing fraction is the fraction of volume in a crystal structure that is occupied by atoms. It is dimensionless and always less than unity. For practical purposes, the APF of a crystal structure is determined by assuming that atoms are rigid spheres. For one-component crystals (those that contain only one type of atom), the APF is represented mathematically by where Natoms is the number of atoms in the crystal, Vatom is the volume of an atom, and Vcrystal is the volume occupied by the crystal. The fig. of a primitive unit cell for the body-centered cubic (BCC) crystal structure is given below.

BE Curve : 

BE Curve The key to energy production in stars lies in what nuclear physicist the curve of binding energy . this plot shows the amount of binding energy per nucleon(a nucleon is either a neutron or a proton . the energy unit is MeV, a standard unit of energy in nuclear physics. This curve indicates how stable atomic nuclei are , the higher the curve the more stable the nucleus

Conclusion :