Binding Energy Formula

Energy equivalent to mass defect is termed as binding energy. A nucleus is like an inflexible spherical ball moulded by getting together a huge amount of miniature spherical balls in the nucleons form. Something is required to bound the nucleons collected. It is that something which assists as the glue. Every nucleon has to donate some of its mass, to deliver the energy resulting in a mass defect.

Binding Energy is also defined as the energy required to break down a nucleus into its component nucleons.

Binding Energy is expressed in terms of kJ/mole of nuclei or MeV’s/nucleon.

Binding Energy Formula

Binding Energy = mass defect x c2

where c= speed of light in vacuum

c = 2.9979 x 108 m/s.                                                                               

Solved Examples

Problem 1: Calculate the binding energy per nucleon for an alpha particle whose mass defect is calculated as 0.0292amu.

Given: mass defect = 0.0292amu

Convert the mass defect into kg (1 amu = 1.6606 x 10-27 kg)

Mass defect  =(0.0292  )( 1.6606 x 10-27  )= 0.04848 x 10-27 kg/nucleus

Convert this mass into energy using DE = Dmc2, where c = 2.9979 x 108 m/s.

E = (0.04848 x 10-27)(2.9979 x 108 )2 = 0.4357 x 10-11 J/nucleus

Convert Energy in terms of  kJ/mole 

  • (1 kJ = 1000 J)
  • convert to mole by multiplying with the Avogadro number (6.022 x 1023 nuclei/mol)

Therefore, E = (0.4357 x 10-11)(6.022 x 1023)/1000

Binding Energy E = 2.62378  x 10kJ/mole


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