MASS AND ENERGY.                        topics

As seen, when nuclei are changed, vast amounts of energy are involved through the Strong Interaction. Typically, a nuclear transformation is one million times more energetic than a chemical change - hence the shear devastation a nuclear bomb can create.

"hydrogen bomb" of about 10 million tonnes of TNT equivalent

A chemical "cell" such as an AA used in a CD player, produces about 1.5V. Chemical reactions individually emit about 1~4 eV (electron-volts). Nuclear reactions produce individually ~2 MeV.

( Remember, an "electron-volt" is a tiny amount of energy. It is 1.6 x 10-19 J and is defined by the elementary charge falling through 1 volt. As all charged elementary particles have this charge of 1.6 x 10-19 C, it is highly convenient. Modern accelerators are heading towards 100 TeV - 1014 eV for each elementary accelerated particle ref: CERN, FermiLab, others. A computer monitor or TV operates at about 28 kV so each electron hitting the screen is at 28 keV.)

Mass interchangeability with energy stems from Einstein's Special Relativity. This is incorporated into quantum mechanics. Simply, whereever an emission of energy takes place no matter what format, some mass must be lost. A chemical exothermic reaction emits such a tiny amount of energy, the mass loss is negligible but for nuclear reactions, it certainly is not. An accelerator reverses the process, shear energy reverts to mass when the opposing beams collide.

We replace "Conservation of Mass" and "Conservation of Energy" with

"Conservation of Mass-Energy"

E = mc2       is set up in joules, kg and ms-1. Simple substitution makes clear that 1 kg = 9 x 1016 J

If we go down to "atomic mass units", "u", based on taking the mass of C-12 isotope as precisely 12 u and measure 1 u in kg using a mass spectrometer

1 u = 1.66 x 10-27 kg , a little less than the mass of a proton.

Substitute in Einstein's equation to get

1 u = 1.49 x 10-10 J = 931 MeV       This is a wonderfully simple conversion if we do all of our arithmetic in amu instead of kg.

Useful masses

proton = 1.007276 u

neutron = 1.008665 u

electron = 0.000549 u

Strictly, all protons, neutrons and electrons should be accounted for when calculating mass/ energy in nuclear equations. Because of the small mass of the electron, sometimes we do not.

BINDING ENERGY & MASS DEFECT

When assembling a nucleus, there is a net release of energy. The total mass of an atom is LESS than the total mass of its parts.

Mass defect = (mass of parts of atom) - (mass of atom)         usually carried out in amu.

Binding Energy is this mass in energy terms and represents the total energy required to pull apart the atom to its separate particles

eg H-2 , the deuterium isotope of hydrogen.

Rest mass of electron          = 0.000549
Rest mass of proton            = 1.007276
Rest mass of neutron           = 1.008665
Total free mass                   = 2.016490

Mass of H-2 atom              = 2.014102
Mass defect                        =0.002388 u

Thus the Binding Energy = 931 x 0.002388 = 2.22 MeV

When a neutron is captured by H-1 to create H-2, a gamma photon of energy 2.22 MeV is released.

BINDING ENERGY PER NUCLEON

Going through all the isotopes and dividing each one's BE by the number of nucleons gives a curve which has a maximum around Fe-56. This element has a very stable nucleus. To create nuclei up to this element, fusion processes continue to release energy but beyond this point, energy is required assembling further nucleons. Fission of larger nuclei releases energy, fusion of lighter elements releases energy.

Stars fuse protons into elements up to Fe-56 releasing energy but heavier elements need energy - from supernovae!

Guess where the heavier elements of Earth originate?

CONSERVATION OF MASS ENERGY   -    MASS DIFFERENCE

To calculate energy released or required in a nuclear reaction of any kind, we simply add all masses before and after.

Mass Difference = Total mass "before" - Total mass "after"

We can then simply convert to MeV.

Consider the nuclear collision when an alpha particle collides with N-14.

Mass Before   Mass After  
He  4.00260 H 1.00783
N 14.00307 O 16.99913
Total 18.00567   18.00696

In this case the mass AFTER reaction is greater than before! The alpha particle MUST have adequate kinetic energy for this reaction to proceed!

Mass Difference = 18.00567 - 18.00696 = - 0.00129 u

Energy required = 931 x 0.00129 MeV = 1.20 MeV