# 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 = mc^{2} 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 ^{2}H[edit]

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

*m*_{proton}= 1.007276 u (where u represents the Atomic mass unit ≈ 1.66053886 x 10^{-27}kg)*m*_{neutron}= 1.008665 u- m
_{proton}+ m_{neutron}= 1.007276 + 1.008665 = 2.015941 u

The mass of the deuteron is:

- Atomic Mass
^{2}H = 2.013553 u

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

### Binding Energies of Isotopes[edit]

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.