NUCLEAR MATHEMATICAL MODEL

ATOMIC ENERGY

Atoms exist in unstable forms called radioactive isotopes. They are the 
atomic equivalents of an old wobbly buildings; sooner or later, they are 
bound to fall apart, splitting into bits like a large building tumbling to the 
ground and releasing energy on the way.

When large atoms split into one or more smaller atoms, giving off other particles and energy in the process, we call it nuclear fission. That's because the central part of the atom (the nucleus) is what breaks up and fission is another word for splitting apart.

It also involves radioactive decay (the conversion of unstable, radioactive isotopes into stable atoms that aren't radioactive).

MASS-ENERGY RELATIONASHIP

Einstein’s Theory of Relativity provides the theory how many joules you get if you turned a kilogram of mass into pure energy.

E = mc²                       

where  E=Energy

           m=mass of atom

            c= speed of light

The main point is, since there are billions and billions of atoms in even a tiny spec of matter, it should be possible to make lots of energy from not very much at all. This is the basic idea behind nuclear power.

NUCLEAR REACTION

Chain reaction is when radioactive isotopes automatically splitting themselves producing energy in the process.

Nuclear Reaction is a process in which changes in atomic nuclei occurs as a result of collision between nuclei and/or nuclear particles.

Nuclear Fission is the process in which heavy nucleus splits into two fragments, once being bombarded with neutron. The splitting of nucleus releases considerable amount of energy with the emission of extra neutron and gamma rays.

Figure: Nuclear Fission Process

(1)neutron is fired, targeting the U-235 nucleus, (2) the U-235 nucleus absorbs the neutron forming the excited compound nucleus U-236, (3) the exited U-236 breaks into two fission fragments with releasing energy and emitting neutrons, (4) the emitting neutron is absorbed by other U-235 nucleus, (5) the same process is repeated where a hugely energetic CHAIN REACTION occurs.

ATOM DENSITY FORMULA

The Atom density is the number of atoms of a given type per unit volume of the material. To calculate the atom density of a substance use these equation.

N=pNa/M = atom/cm^3

where :

N = Atom density (atom/cm^3)

p = density (g/cm^3)

Na = Avogadro's Number (6.022 10^23 atoms/mole)

M = Gram atomic weight

Slowing Down the Fast Neutron

taverage=tpromt (1-B) + tdelayed (B)