# Working out the mass defect and binding energy of He-4.

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Working out the mass defect and binding energy of He-4

The mass of a He-4 atom is 4.002603 u 1 u = 1 atomic mass unit = 1.66054.10 -27 kg A Helium atom includes 2 electrons each 0.000549 u We need the mass of the nucleus This mass is equal to: 4.002603 - (2 x 0.000549) = 4.001505 u.

The mass of a proton is 1.007276 u The mass of a neutron is 1.008665 u Added these 4 particles have a mass of 2 x 1.007276 + 2 x 1.008665 = 4.031882.

A He-4 nucleus has mass 4.001505 u 2 protons and 2 neutrons have mass 4.031882 u This is weird! Together, in a nucleus, the mass is smaller. So when you create a He-4 nucleus from 2 protons and 2 neutrons some mass disappears. This ‘missing mass’ is called the mass-defect  m = 4.031882 - 4.001505= 0.030377 u.

The mass–energy equivalence arose originally from special relativity, as developed by Albert Einstein, who proposed this equivalence in 1905 in one of his papers entitled "Does the inertia of an object depend upon its energy content?" The equivalence of energy E and mass m is described by the famous equation:  E =  m.c 2.

The mass defect of He-4 is 0.030377 u Change this to kg: 0.030377 x 1.66054.10 -27 = 5.044222.10 -29 kg Use E = m.c 2 to find the energy equivalent  E = 5.044222.10 -29 x (2.997928.10 8 ) 2 =  E = 4.533531.10 -12 J 1 MeV = 1.602177.10 -13 J  E = 4,533531.10 -12 / 1.602177.10 -13 =  E = 28.3 MeV.

The binding energy of He-4 is 28.3 MeV This energy is needed to separate the 4 particles in the nucleus This is the energy that is released when a He-4 nucleus is created High binding energy = stable nucleus Mass disappears, energy appears The binding energy per nucleon of He-4 is 28.3 / 4 = 7.1 MeV per nucleon.

Step 1 – Find the mass of the nucleus Step 2 – Find out how many protons and neutrons you need to build the nucleus and calculate their total mass Step 3 – Calculate the mass-defect Step 4 – Calculate the binding energy (per nucleon) using 1 u=931.5 MeV.

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