Nuclear Physics Concept Page - 7

Definition

Nuclear density

Nuclear density is the density of the nucleus of an atom, averaging about 2.3×1017 kg/m3$2.3\times {10}^{17}kg/m^3$.
The density of a nucleus in which mass of each nucleon is 1.67 ×10−27$\times {10}^{-27}$ kg and Ro=1.4×10−15${}_o=1.4\times {10}^{-15}$ m is
Given
MN=A×1.67×10−27kg$M_N=A\times 1.67\times {10}^{-27}kg$......where A = mass number
R0=1.4×10−15m$R_0=1.4\times {10}^{-15}m$
Nuclear Volume, VN=43π[(R0)3(A13)3$V_N={\displaystyle \frac{4}{3}}\pi [(R_0{)}^3(A^{{\displaystyle \frac{1}{3}}}{)}^3$
VN=43π[(R0)3A$V_N={\displaystyle \frac{4}{3}}\pi [(R_0{)}^{3}A$
The nuclear density is
ρN=Mass of nucleusNuclear volume${\rho }_N={\displaystyle \frac{\text{Mass of nucleus}}{\text{Nuclear volume}}}$
ρN=A×1.67×10−2743π[(R0)3A${\rho }_N={\displaystyle \frac{A\times 1.67\times {10}^{-27}}{\frac{4}{3}\pi [(R_0{)}^{3}A}}$
ρN=3×1.67×10−2712.56×(1.4×10−15)3${\rho }_N={\displaystyle \frac{3\times 1.67\times {10}^{-27}}{12.56\times (1.4\times {10}^{-15}{)}^3}}$
ρN=5.01×10−2734.46464×10−45=1.453×1017kgm−3${\rho }_N={\displaystyle \frac{5.01\times {10}^{-27}}{34.46464\times {10}^{-45}}}=1.453\times {10}^{17}kg{m}^{-3}$

Definition

Nuclear reaction vs Chemical reaction

Here are the following differences between chemical reactions and nuclear reaction.
1. While nuclear reaction takes place in the atoms nucleus, the electrons in the atom are responsible for Chemical reactions.
2. The chemical reactions involve the transfer, loss, gain and sharing of electrons and nothing takes place in the nucleus. Nuclear reactions involve the decomposition of the nucleus and have nothing to do with the electrons.
3. In a nuclear reaction, the protons and neutrons react inside the nucleus and in chemical reactions the electrons react outside the nucleus.
4. When comparing the energies, a chemical reaction involves only low energy change, where as a nuclear reaction has a very high-energy change.

Definition

Mass Energy Equivalence

The "mass-energy equivalence" principle states that the mass of a system and its energy are the same property in any physical system.
This means that anything having mass has an equivalent amount of energy and vice versa.

Definition

Relationship between mass and energy

By the theory of special relativity Einstein showed that mass is another form of energy and one can convert mass-energy into other forms of energy, say kinetic energy and vice-versa.Einstein gave the famous mass-energy equivalence relation
E=mc2$E=m{c}^2$
where c=3×108m/s$c=3\times {10}^{8}m/s$ is the speed of light.

Example

Energy equivalent of mass

Energy released if mass of 2 amu is converted into energy isE=Δmc2$E=\mathrm{\Delta }m{c}^2$
    =(2×1.67×10−27kg)×(3×108ms)2$=(2\times 1.67\times {10}^{-27}kg)\times (3\times {10}^8\frac{m}{s}{)}^2$
    =3×10−10J$=3\times {10}^{-10}J$

Definition

Pair production and annihilation

Pair production is the creation of an elementary particle and its antiparticle, for example creating an electron and positron, a muon and antimuon, or a proton and antiproton. Pair production often refers specifically to a photon creating an electron-positron pair near a nucleus but can more generally refer to any neutral boson creating a particle-antiparticle pair. In order for pair production to occur, the incoming energy of the interaction must be above a threshold in order to create the pair, at least the total rest mass energy of the two particles and that the situation allows, both energy and momentum to be conserved.There exists an inverse process to pair production called pair annihilation, in which a particle and its antiparticle collide and annihilate each other, the total energy of the two particles appearing as electromagnetic radiation.

Definition

Mass defect

The difference in mass of a nucleus and its constituents, ΔM$\mathrm{\Delta }M$, is called mass defect and is given by
ΔM=[Zmp+(A−Z)mn]−M$\mathrm{\Delta }M=[Z{m}_p+(A-Z)m_n]-M$

Definition

Binding energy and binding energy per nucleon

If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy Eb$E_b$ will be released in the process. The energy Eb$E_b$ is called the binding energy of the nucleus.
Eb=ΔMc2$E_b=\mathrm{\Delta }M{c}^2$
The ratio of the binding energy Eb$E_b$ of a nucleus to the number of the nucleons, A, in that nucleus is called the binding energy per nucleon, Ebn$E_{bn}$.
Ebn=EbA$E_{bn}={\displaystyle \frac{E_b}{A}}$

Definition

Variation in binding energy per nucleon with mass number

• The force is attractive and sufficiently strong to produce a binding energy of a few MeV per nucleon.
• The constancy of the binding energy in the range 30 < A < 170 is a consequence of the fact that the nuclear force is short-ranged.
• A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. Thus if a nucleus A = 240 breaks into two A = 120 nuclei, nucleons get more tightly bound. This implies energy would be released in the process.
• Consider two very light nuclei (A≤$\le$10) joining to form a heavier nucleus. The binding energy per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei.This means that the final system is more tightly bound than the initial system. Again energy would be released in such a process of fusion.

Definition

Exoergic and Endoergic Reactions

Nuclear reactions are reactions in which either two nuclei collide with one another or a small particle such as a neutron collides with the nucleus of some atom.
Nuclear reactions can be described using energy changes as follow :
An exothermic (exoergic) nuclear reaction is a reaction that releases energy while an endothermic (or endoergic) reaction is one that requires an input of energy to take place.
The changes in kinetic energy during a nuclear reaction is defined as the reaction energy (or Q-value).
If the reaction energy is positive, the reaction is exothermic but if the reaction energy is negative, the reaction is endothermic.

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