BETA DECAY

There are 3 models of beta radioactivity

i) Negatron (β^-) Emission

ii) Orbital Electron Capture

iii) Positron (β⁺) Emission

BETA SPECTROSCOPY

Beta ray spectra is of two types:

i) Continuous Spectrum

ii) Sharp Line Spectrum

The continuous spectrum is due to Negatrons and Positrons.

There is a possibility of the daughter nucleus being created in an excited state, which may decay by gamma emission.

Rutherford suggested that part of gamma radiation is absorbed by outer electrons of same atom and as a result the secondary beta ray electrons are ejected.  The process is called “Internal Conversion”.

The sharp Line Spectrum is due to secondary beta rays emitted due to internal conversion.

The process of Beta disintegration differs from alpha disintegration in following two respects:

i) The alpha particles are already present in the initial nucleus while beta particles are not present in the initial nucleus. Beta particles are created at the time of emission.

ii) The energy spectrum of alpha particles is discrete while energy spectrum of beta particles is continuous.

iii) Beta decay is a three body problem while alpha decay is a two body problem.

In the Neutrino, the spin and angular momentum vector are oppositely directed and in anti neutrino these vectors are aligned together.

Since a matter-antimatter pair is formed whenever energy is converted into mass, in a conversion of a nuclear Neutron to a Proton, the negative electron (matter) should accompany anti neutrino (anti matter). Similarly Neutrino is emitted with positron emission and orbital electron capture.

FERMI THEORY OF BETA DECAY

In 1934, Fermi made a successful theory of beta decay. The theory is based on following assumptions:

1) The light particles, the electron and neutrino ar created by transformation of a neutron into a proton in a nucleus or vice versa.

Note:- Neutron or Proton that are transformed to beta particles are not free particles but are bound to Nucleus by Nuclear Forces.

2) The energy remains conserved in decay process, the available energy being shared among the electron and the neutrino.

3) The beta decay process is analogous to the emission of electromagnetic radiation by an atom, with electron-neutrino field acting in place of Electromagnetic field.

4) “Electron-Neutrino” field is weak in contrast to short range strong interactions which exist between Nucleons bound in the nucleus.

5) Time   Dependent Perturbation theory is a very good approximation because of smallness of coupling constants.

6) As Nucleons move with velocities of only nearly c/10 in nuclei calculations can be made with non relativistic nuclear wave functions.

What is Covalent bonding?

The covalent bond is formed by sharing of pairs of valence electrons between like atoms rather than by electron transfer.
eg : consider the hydrogen molecule H2 ; when two isolated 'H' atoms, each with its electron in the ground state 1S orbital approach each other , the 1S clouds begin to overlap. Each electron is attracted to the other nucleus and the overlap increases( provided the electrons have opp spin) . The two atomic orbitals merge into a molecular orbital. when the repulsive forces have been balanced the attractive forces a molecule results , having stability greater than that of two isolated atoms.
The covalent bonding is also known as "Home polar" or "electron - pair bonding".

Saturation in covalent bonds
   Hydrogen molecule can be stable with only two atoms. If a third atom is brought near 'H2' it is repelled due to allowed exchange of spins is repulsive.Thus covalent bond exhibits.

Direction nature of Covalent bond
    The covalent bond is formed as a result of pairing of two electrons in the atomic orbitals of two atoms, the bond then should lie along the direction of overlapping of atomic orbitals.Hence covalent bonds will have strong preferences.

Hybrid bonding
         Covalent bonds are not only formed by pure 'S' orbitals or pure 'P' orbitals but can also be formed by the overlapping of 'S' and 'P' orbitals called hybrid bonding. eg:- H2O; The HOH bond angle is 104.5 deg  

NEUTRON DIFFRACTION

X-Ray diffraction techniques have certain limitations. In 1936, "W M Elgasser" suggested that moving Neutrons should have debroglie waves associated with them and therefore could be diffracted. The debroglie wavelength of Neutron moving with most probable speed at 20 is 1.80. this is of order of interplanar spacing in crystals. so neutrons can be diffracted by crystals and can be used to study their structure.
          A beam of thermal neutronsfrom an atomic pile possessing all wavelengths is collimated and allowed to fall upon a single crystal. The diffracted beams are photographed on a photographic plate. A Laue pattern is obtained. The Laue pattern can be used to study the crystal structure. The Laue pattern with Lead clearly shows the greater transparency of matter to Neutrons than X-Rays.

The diffraction patterns are formed in a way similar to that for X-rays. For X-rays of 1Amstrong, one requires energies of order 10^4 eV and for electrons about 10^2 eV.

Neutrons are scattered chiefly by Nuclei of atoms, and since wavelength of Neutrons is much greater than dimensions of scattering nucleus, the atomic scattering factor is nearly independent of  scattering angle. Experimentally it was observed that when a beam of Neutrons from a Radium Beryllium source was diffracted by MgO crystal, a maximum occured where predicted by Bragg's relation. The scattering crossection of Nuclei for thermal Neutrons does not depend on atomic number of element, as it does for X-rays.

The scattering of X-Rays by light elements is relatively weak because X-Ray scattering is done by electrons. The Neutrons can penetrate into the matter very easily enables us to deduce the positions of Hydrogen and Carbon atoms in a number of organic crystals.

A major role of Neutron Diffraction has been investigating the magnetic structure of solids. This is a result of fact that Neutrons possess magnetic moments and that these magnetic moments interact with magnetic moments of scattering atoms of solid. This gives an additional scattering mechanism for Neutrons which often outweighs Nuclear Scattering.

If the atomic moments are randomly oriented as in a paramagnetic solid, the magnetically scattered Neutrons are incoherent in phase leading to a diffuse background. This diffuse background of magnetic scattering is then super imposed on lines produced by scattering.              

What are Super Conductors?

Certain Metals when cooled, their electrical resistance decreases in usual way as in normal conductors, but on reaching a temperature a few degrees above absolute zero they suddenly lose all trace of electrical resistance. Then they are said to have passed into superconducting state.

Kamarlingh Onne was the first to observe this peculiar property in case of Mercury in 1911. In the course of his investigation of electrical resistance of a sample of Mercury dropped from 0.08Ω at about 4K to less than 3x10-6Ω over a temperature interval of 0.01K.

Super Conductors are extra ordinary because they take no energy at all to make current flow in a conductor and no energy is lost to friction to sustain the current either. Its electrical resistance is precisely zero.

Critical or Transition Temperature

One of the important characteristic property of super conductors is that their electrical resistance, for all practical purposes is zero below a well defined temperature T_c, called Critical or Transition Temperature. For instance, semiconducting mixed oxides of Barium, Lead and Bismuth.

Important Properties of Super Conductors

1. The current in super conductors persists for a very long time.

2. The magnetic field does not penetrate into the body of super conductor. This property known as Meissner Effect is fundamental characterization of super conductivity.

3. When the applied magnetic field ‘B’ is greater than Critical value B_c(T), the super conductor becomes a normal conductor.  B_c(T) is zero at T=Tc and has the largest value at T=0.

4. When the current through Super Conductor is increased beyond a Critical value I_c(T), Super Conductor becomes a normal conductor.

5. Specific heat of the Super Conducting materials shows an abrupt change at T=T_c jumping to a larger value for T<T_c.  

Effect of Magnetic Field on Super Conductors

   The super conducting state of metal exists only in a particular range of temperature and field strength. Super conductivity state will disappear if the temperature of specimen is raised above its critical temperature Tc or if a sufficient strong magnetic field is employed.

The critical field for which super conducting property loses is a function of temperature.

Hc =H0[1-(T/Tc)^2]

Where

Hc is Maximum Critical Field Strength at temperature T

H0 is Maximum Critical Field Strength at temperature absolute zero.

Tc is Critical Temperature, the highest temperature for super conductivity

The Meissner Effect
 

    Superconductors which are resistance less materials have an additional property of exclusion of applied magnetic field on it i.e. inside a superconducting material, we always have B=0.





 

    The property of perfect diamagnetism arises in super conductor because when a magnetic field ‘Ba’ is applied surface screening currents circulate so as to produce a flux density ‘Bi’ which every where inside the metal exactly cancels the flux density due to applied field Bi=-Ba.

For a Super Conductor μ_r=0; i.e. B=μ_rB_a=0

This property of exhibiting perfect diamagnetism by super conductor is known as Meissner Effect.

 

PAULI's NEUTRINO HYPOTHESIS

Pauli postulated the existence of new particle, “Neutrino” as early as in 1930. According to Pauli, an additional particle called a neutrino denoted by ‘ν’ is emitted in process of β-decay.

This particle according to Pauli, carries away an amount of energy equal to difference between the observed energy for a β-particle and maximum energy of continuous beta spectrum. The principle of conservation of energy is thus satisfied.

To satisfy Principle of Conservation of Angular Momentum, Neutrino must be assigned following properties

i) It must have zero charge; because in a β-decay process the charge is conserved without neutrino. Also if Neutrino is charged, it would produce ionization which certainly could have been detected. Zero charge in turn implies negligible magnetic moment.

ii) It must have zero or almost zero mass: the mass-energy balance of β-decay processes shows that neutrino rest mass is negligible.

iii) It must have a spin of ½: This will satisfy Law of Conservation of Angular Momentum in β-decay process. Further Neutrino must be a Fermion, so that nuclear statistical requirements are fulfilled.

iv) A neutrino has an antiparticle called anti-neutrino which has zero rest mass, zero charge and spin-1/2.