Material Properties Lecture (2) PDF

Dr. Marwa Mostafa 1. Thomson’s plum pudding atomic model 2. Rutherford’s nuclear atomic model 3. Bohr’s quantum atomic model 4. Sommerfeld’s relativistic atomic model 5. Wave mechanical or de Broglie’s atomic model, or modern concept of atomic model.  Bohr conceived-off a new atomic mode...

Dr. Marwa Mostafa 1. Thomson’s plum pudding atomic model 2. Rutherford’s nuclear atomic model 3. Bohr’s quantum atomic model 4. Sommerfeld’s relativistic atomic model 5. Wave mechanical or de Broglie’s atomic model, or modern concept of atomic model.  Bohr conceived-off a new atomic model employing the principles of quantum theory suggested by Planck.  This model provided adequate explanation for stability of the atom.  Bohr postulates: He proposed new ideas which are now known as Bohr’s postulates. These are:  i. Electrons revolve in non-radiating stationary orbits. Centripetal force provided by Coulomb’s force of attraction between the electron and the nucleus keeps the electron in orbital motion,  𝒎𝒗𝟐 𝟏 (𝒁𝒆)(𝒆)  = 𝒓 𝟒𝝅𝝐𝟎 𝒓𝟐 where, Z = atomic number of nucleus, m = mass of the electron, v = velocity of electron in the orbit, r = radius of the orbit, e = charge of electron.  ii. Angular momentum of the moving ℎ electron is an integral multiple of where h 2𝜋 is Planck's constant 𝑛ℎ 𝑚𝑣𝑟 = 2𝜋  where, n = 1, 2, 3,... ∞, and is called principal quantum number.  iii. The electron does not radiate energy while moving in stationary orbit.  Energy is emitted when the electron falls from higher energy orbit to lower energy orbit. If the electron jumps-up to higher energy orbit from lower energy orbit, absorption of energy takes place.  The energy absorbed or emitted is expressed by Bohr’s frequency condition given as   Δ E = Ef – Ei = hf where f is the frequency of emitted radiation, Ei and Ef are the energies of initial and final orbits respectively.  Energy of an electron is the sum of kinetic energy Ek due to its motion and potential energy Ep due to its position in the orbit.  The potential energy of an electron is equal to the work done in bringing the electron from infinity to the present position.  This work is required to be done due to Coulombian force produced by the nucleus.  The modern concept of atom also considers the concept of wave nature of electron.  According to this concept a particle (say electron) of mass m moving with velocity v is associated with a wave propagating in the direction of moving particle.  This wave is known as de Broglie wave or matter wave.  Wavelength λ of such a wave associated with the particle is given by ℎ 𝜆= 𝑚𝑣  Velocity of electron accelerated by a potential difference of V volts can be obtained from: 2𝑒𝑉 𝑒𝑉 = 0.5 𝑚𝑣 2 , 𝑣 = , 𝑚𝑣 = 2𝑚𝑒𝑉 𝑚  If we try to break a material, it requires application of some breaking force.  The magnitude of applied force varies widely for different materials. A chalk may break by applying a small force; timber may require application of medium magnitude of force, but steel necessitates application of substantial external force.  In fact, atoms in the solids are held together by internal forces. These forces are known as bonding forces or atomic bonding forces or chemical bonding forces.   Valence and Free Electrons  Electrons play vital role in determining electrical properties of metals.  Valence electrons in the outermost orbit of an atom decide the manner in which they respond to external effects.  For example, due to their free movement within the metal they provide conduction, but on actuation by thermal energy they jump over the energy gap in semiconductors.  As a whole the arrangement of electrons in an atom, behavior of valence electrons, and interatomic interactions govern the electrical properties (conduction as well) of materials.  Various electron theories have been propagated to study the behavior of solids: 1. Drude-Lorentz (classical) theory, 2. Free electron theory, 3. Energy band theory, and 4. Brillouin zone theory.  The electrons in the outermost orbit are not bound to its atom, and are free to move throughout the solid.  These free electrons are known as Fermi gas or electron cloud.  The free electron theory is based on the assumption that the total energy E is equal to the kinetic energy Ek only. 1 𝐸 = 𝐸𝑘 = 𝑚𝑣2 2  Kinetic Energy in Terms of Wave Number ℎ2 𝑘2 𝐸= 2 8𝜋 𝑚  Defining the wave number k by: 2𝜋 𝑘= 𝜆  Potential energy of an electron is a function of its position with respect to the ion-cores.  The potential energy of an electron cannot be neglected as compared to its dimension.  The probability of finding an electron remains maximum at the crest of the waveform.  The energy will be given by E=Ek+Ep  The two possible waveforms are sine wave and cosine wave, formed due to the superimposition of travelling de Broglie waves.  Atomic bonding