# Nuclear Physics/Nuclear Binding Energies

Binding energy is the amount of energy required to separate something down into its base components. In nuclear terms, the energy is derived from the Strong Nuclear Force.

The binding energy must come from somewhere, and in the case, because mass and energy are so strongly linked by Einstein's Equation E = mc2 the Binding Energy is proportional to the Difference in Mass of the Atom, compared to the sum of its parts. This is also called the mass defect. The larger the mass defect, the more stable the isotope is.

Example of Binding Energy:

### The Binding Energy of a Deuteron 2H

A deuteron is the nucleus of a deuterium atom, and consists of one proton and one neutron. The masses of the constituents are:

mproton = 1.007276 u (where u represents the Atomic mass unit ≈ 1.66053886 x 10-27 kg)
mneutron= 1.008665 u
mproton + mneutron = 1.007276 + 1.008665 = 2.015941 u

The mass of the deuteron is:

Atomic Mass 2H = 2.013553 u

The mass difference = 2.015941 - 2.013553 = .002388 u. = 3.9654 x 10-30 kilograms.

 $E\,$ $=m c^2\,$ $=3.9654 \times 10^{-30} kg \times (2.99792458 \times 10^{8} m s^{-1})^2$ $=0.3564 \times 10^{-13} J$ $=2.224 MeV\,$

### Binding Energies of Isotopes

Iron is one of the most stable nuclei around. A picture should really be added here.

but if h= 1.007277, then 2h= 2.0014554 and the difference between p and n is .001388. when you add this difference you get 2.0028434=2h.

try this h=1,007825,n=1.008665 then 2h =2.01565 and 1.008665-1.007825=.00084 then add that difference to change p to n, so 2.01565+.00084=2.01649 now sub. the so call binding energy, 2.01649-.002388= 2.014102 and this is mass of 2d that I find in text books!!! also .002388u mult. by 931.5 = 2.224422 in MeV units! if you follow the above 2.014102 times 2 is 4.028204. and 3 times 4.028204 is 12.084612, this is carbon. 12carbon(12.084612) + 1.007825 = 13nitrogen(13.092437) + .00084 = 13.093277(before the loss of a +beta and neutrino!). 13.093277 - .002388 = 13carbon(13.090889), add 1.007825 to get 14nitrogon(14.098714). again add 1.007825 to get 15oxygen(15.106539). again add .00084 to get 15.107379(again this is before loss of a +beta and neutrino!). again subtrack .002388 to get 15nitrogen(15.104991). now add 1.007825 to get 16oxygen(16.112816).

 16oxygen(16.112816) = 12carbon(12.084612) + 4helium(4.028204) and this is the carbon cycle in stars.


in Frontier's note: the proton is 1.007277, and Hydrogen is 1.007277+(+beta=.000548)= 1.007825. Also .002388= (2(+beta)+2(-beta)+2(.000098)) or .002388=(.001194+.001194)=((.000548)+(.000548)+(.000098))x2, that is in a world with perfect field breaking symmetry, in fusion this happens 1.007825 + (1.007825 + .000840) = 2.01649.

 Ok, look this .002388 - .000840 = .001548, .000840 = .000548(first beta) + .000292,
and .000292 = (.000098 + .000098 + .000096),
and .001548 = (.001096(.000548x2)(second and third) + .000452),
now add .000096 + .000452 = .000548(fourth).
When betas are formed they do so in pairs (one real, one virtual), so do neutrinos = .000098.


Now take 2.016490-1.006985(too light)=1.009505(too heavy). To 1.006985(tl) add .000292= 1.007277 add .000548= 1.007825 add (.000292+.000548)=.000840= 1.008665 add .000840= 1.009505(th). And if 1.006985/3= .3356616667 add .000840= .3365016667*3= 1.009505. .3356616667*931.5= 312.6688425, .3365016667*931.5= 313.451325, and 312.6688425 + (2*313.4513025)=939.5714476/931.5= 1.008665.