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Home » Physics Homework Help » Nuclear Physics
Nuclear Physics
Isotopes

Elements having same atomic number Z, but different A mass number for example 126C, 146C and 11H, 21H, 31H are isotopes of carbon and hydrogen.

Isotones

Elements having same number of neutrons (N) but different atomic number for example (Z) 42He, 31H.

Isobars

elements having same mass number (A) but different atomic number (Z) are called isobars, for example, 146C 147C are isobars. Protons and neutrons together are called nucleons.

Stability Criterion

A survey of periodic table carefully reveals that those elements in which N / Z = 1 or 1.6 are stable. Amongst these, the elements having even N and even Z are the most stable and are termed as magic numbers.

The heaviest stable nuclide is 2009Bi83. Lend (2008pb82) is the most stable heaviest element. All transuranic elements finally disintegrate into lead (Pb). The elements or nuclides which decay with time are termed as radioactive nuclides.

The element / nuclide, whose binding energy per nucleon is less than 7.5 MeV, are (mostly) unstable.

Nuclear radius

R = R0A1/3 where R0 = 1.1 x 10-15 m or 1.1 fm.

Note that the density within a nucleus is independent of mass number.

Nuclear spin

All nucleons (protons or neutrons) are spin particles. They have spin odd half multiple of h = (h/2π) they follow Fermi disc statistics or Pauli’s exclusion principle and are called fermions.

Nuclear force
 
Is a short range force extending upto 10 fm. It is fifty-sixty times stronger than electromagnetic force. Nuclear force is independent of charge. Nuclear force between two protons is same as nuclear force between two neutrons or nuclear force between a proton and a neutron. It is not a central force. It cannot be solely determined by distance. It depends upon the spins of the nucleons as well.

Heisenberg in 1932 proposed exchange force theory. Yukawa extended this theory and calculated mass of π - mesons. According to this theory, proton does not remain proton forever and similarly neutron does not remain as neutron forever. They go on changing for instance.

10n ↔ 10n + π0; 11p ↔ 10 n + π+;

10n ↔11b +  ; 11p ↔ 11p +π
0

Where π0, π+ and π are π - mesons having mass around 200 me, later on π - mesons were confirmed in cosmic rays. The heavy nuclides require more neutrons so that coulomb repulsion between protons could be balanced by nuclear force.

Binding energy B = (Z mp + Nmn – M) c2 where M is mass of the nucleus. The term in the bracket is called mass defect. Binding energy per nucleon

B/A = (Zmp /P + Nmn/A – M/A) c2

Mass excess let A be the mass number of a nucleus. Let mu (atomic mass units) be the mass of neutral atom and au is mass of the nuclide in amu then excess mass

= (mu – au)

= (m – a) 931.5 / c2 MeV x c2

= (m – a) 931.5 MeV.


Packing fraction P = (m – A)/A

Binding energy is the algebraic sum of volume energy surface energy and coulomb energy

B = a1A + a2A 2/3 – a3 Z (Z – 1) / R

= a1A + a2A2/3 – a3Z (Z – 1) / A1/3


Or binding energy per nucleon

B/A = a1 + a2 /A1/3 – a3 (Z – 1) Z / A4/3

Radioactive decay stable nuclides have definite atomic number and number of neutrons. Unstable nuclides decay by alpha emission or β – emission. When the residual nucleus gets de – excited y – rays are also produced.

Q – Value of the reaction

Q = u1 – uf = (MR – MP) c2 where

MR ---> mass of reactants

MP ---> mass of products

For the a – decay

Q = [m (A/ZX) – m (A-4/Z-2Y) – m (4/2He)] c2

A stream of a – particles coming out from a bulk is called a – rays.

Alpha decay

A/ZX ---> A-4 Z-2Y + 4/2 He

In alpha decay, proton number decreases by 2 and mass number decreases by 4. The residual nucleus is thus different and is termed as daughter nucleus.

Conditions for a – decay mass number A > 210 and N/Z > 1.6.

Three types of β – decay (a) β – (or electron emission), β + (positron emission) and electron capture.

β decay kept scientists puzzled for about 20 years. We consider radioactivity as a collision process. Momentum could not be conserved as emitted β – particles have different energies. It was then suggested consider β – emission as a two particle emission. The second particle was soon detected as a neutrino. Neutrino has rest mass zero. it has a spin quantum number ½

To understand β – emission, we must have an idea of conservation rules.

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