Experimental verification of the dual nature of electrons (matter):
Wave Nature:
a) Davidson and Germer’s experiment showed that electron beams reflected or scattered from a crystal gave a diffraction pattern ( consisting of a number of concentric rings) This phenomenon can be explained only using the wave nature of electrons.
b) Thompson replaced the crystal by a gold foil and performed the above experiment and obtained a diffraction pattern which again confirmed the wave nature of electrons.
Particle nature
a) Scintillation effect: When electrons strike a Zinc Sulphide screen a spot of light know as Scintillation is produced. This is a localised effect characteristic of particles or matter.
b) Mass of electron and the determination of e/m ratio by Thompson determines the particle nature of radiation.
c) The rotation of the mica wheel by the electron beams in a cathode ray tube is characteristic of particle nature i.e. momentum of the electron is transferred to the paddle wheels.
Theoretical confirmation of the dual nature of matter:
De Broglie's Relation:
In the case of a photon if it is assumed to have a wave character its energy is given by
E = hn (1) According to Planck’s theory where h is Planck’s constant and n is the frequency of a radiation.
If the photon is supposed to have a particle character, its energy is is given by
E = mc2 (2) According to Einstein’s equation
From equations (1) and (2) mc2 = hn
, n = c/l , mc2
= h c/l or l = h/mc
for matter mc = mv where v is the velocity of matter or
l = h/p
p = momentum of an electron.
Quantum Numbers:
These are a set of 4 integers necessary to specify the energy , position, shape , size and orientation of orbitals to which electrons belong.
Principal Quantum Number ‘n’ :
It specifies the location and energy of an electron, It is a measure of the effective volume or size of the electron cloud denoted by ‘n’ and can have values 1,2,3,4..........¥
Azimuthal Quantum Number ‘l’ :
It determines the shape of the orbital. It takes
integral values from 0 ® (n-1) where ‘n’
is the principal quantum number. When ‘l’ = 0, 1, 2, the shapes of the
orbitals are ‘s’ Spherically symmetrical, ‘p’ dumbbell, and ‘d’ double
dumbbell.
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Angular momentum = Ö l( l + 1 ) x h / 2p
It gives the orientation of the orbitals in space. It takes integral values ranging from -l ......0 .....+l or ‘s’ orbital has got one orientation, ‘p’ orbital has got 3 orientations, ‘d’ orbital has got ‘5’ orientations and ‘f’ orbital has got 7 orientations.
Spin Quantum Number ‘s’ :
It indicates the direction in which the electron spins on its own axis or the magnetic property that is associated with it . This value is quantised the two vlues that are permitted are + ½ and - ½ where g = gyromagnetic constant. m = g x Ö s(s + 1)
Heisenbergs Uncertainty Principle:
It is impossible to measure simultaneously the position and momentum of a small particle (subatomic particle) with absolute accuracy or certainty
What is the significance of the uncertainty principle ?
Why the electron cannot exist in the nucleus?
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| It is a well defined circular path around the nucleus in which the electron revolves | It is a region in three dimensional space around the nucleus where there is a very high probability of locating the electron |
| It is circular in shape | ‘s’, ‘p’ and ‘d’ orbitals are spherical, dumbbell and double dumbbell in shape respectively |
| It represents the movement of an electron around the nucleus in one plane. | It represents the movement of an electron around the nucleus in a three dimensional space. |
| It states with certainty the momentum and position of an electron. Violates the Heisenbergs uncertainty principle | It is a consequence of Heisenbergs uncertainty principle. .i.e. The position and momentum cannot be known with certainty |
| The maximum number of electrons in an orbit is 2n2 . | The maximum no of electrons in an orbital is 2 |
The number of orbitals = n2
Degenerate Orbitals:
The orbitals of the same subshells having equal energy are called degenerate orbitals.
e.g. Px, Py and Pz orbitals. The 5 ‘d’ orbitals are degenerate but can loose their degeneracy under the influence of and external electrical or magnetic field.
Nodal Plane:
The plane passing through the nucleus on which the probability of finding the electron is almost zero is called Nodal plane
Schrodinger Wave Equation:
‘E’ is the total energy of the electron in the
system and ‘V’ is the potential energy of the system.
Y
It is known as an orbital wave function which is a solution
to the Schrodinger wave equation. It represents the amplitude of the wave
and the significant values are Eigen functions.( The wave function Y
by itself has no significance)
Y 2
It represents the electron density or the probability of locating electrons
of specific energy at different regions in space. It leads to the concept
of orbitals.
Energy of the electron in the ground state of hydrogen atom:
E = -2.17 x 10-18 J/Atom and -1.312x106 J/Mole.
Why is the value of the energy of an electron negative?
The value of the energy of an electron in the hydrogen atom is negative because when the electron is far away from the nucleus the Potential Energy is taken as zero. When the electron comes closer to the nucleus work is done by the electron therefore energy is released and the energy of the electron becomes less than zero hence it has a negative value.
The difference in Energy between two energy levels viz. E2 and E1 when E2 > E1:
E2 - E1 = D E
(D E is -ve)
D E = hn
The study of quantum numbers may be briefly summarised as follows:
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‘n’ |
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‘s’ |
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Electronic Configuration of Elements:
Aufbau Principle:
According to the principle the electrons are filled in the various subshells in the order of their increasing energies.
(n + l) Rule: The subshell with lower n+l value will posses lower energy and will be filled first.
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 4f ......
Pauli’s Exclusion Principle:
No two electrons in an atom can have all the 4 quantum numbers alike.
Hund’s Rule of Maximum Multiplicity:
Electron pairing will not take place in degenerate orbitals (same energy subshell) until each orbital is first singly filled with electrons having parallel spins.
Why is it that the 4s electrons are lost during the formation of divalent ions in the first transition series e.g. Fe2+ & Ni2+?
Cu, Cr, Mo, Ag, W & Au have got exceptional electronic configuration. Explain.
Z = 29, 24, 42, 47, 74 & 79 Respectively.
Half Filled ‘d’ orbital configurations are preferred because
Molecular Orbital Theory
This theory has been proposed by Hund and Mullicken
Basic Concept:
Atomic orbitals of atoms involved in the formation of a molecule get
redistributed to give rise to an equivalent number of new molecular orbitals.
During the process the identity of the atoms are lost. Linear combination
of atomic orbitals leads to the formation of the molecular orbitals.
Bonding Molecular Orbitals ymo
A Constructive Interference leading to Addition Combination of wave fronts.
A Destructive Interference leading to Subtractive Combination of Wave fronts:
It is a measure of the stability of the molecule
It can be calculated by the following relation where Nb stands for the electrons in the bonding molecular orbital and Na stands for the number of electrons in the antibonding molecular orbital. B.O = ½[Nb - Na] We can draw the following conclusions from the values of the bond order:
Paramagnetic Behaviour of Oxygen can only be explained using M.O. Theory
To be continued.....