B.Sc First year chemistry
INORGANIC CHEMISTRY
• Introduction
In the beginning of nineteenth century, John Dalton (1766-1844) put forward his atomic theory, he regarded atom as hard and smallest indivisible particle of matter that takes part in chemical reactions; the atoms of one particular element are all identical in mass and atoms of different elements differ in mass and other properties.
Later on, various investigators around the end of nineteenth century and beginning of twentieth century did several experiments and revealed the presence of much smaller negatively charged particles, named electrons by J.J. Thomson (1897) and positively charged particles, named protons by Rutherford (1911) within an atom. These tiny particles were called subatomic particles. It was also established by Rutherford that the whole positive charge and most of the mass of an atom lies at nucleus. The positive charge on the nucleus
was attributed to the presence of protons called the atomic number by Moseley (1912). The electrons were said to be arranged around the nucleus in the extra nuclear region in certain well defined orbits called energy shells and were said to be in constant motion (N. Bohr,1913). Chadwick’s experiments (1932) also revealed the existence of yet another subatomic particle in the nucleus which did not have any charge and named as neutrons. Further investigations established that there were also present some other subatomic particles in the nucleus in addition to electrons, protons and neutrons. These particles are positrons, neutrinos, antineutrinos, pions (π-mesons) etc. The pions (Yukawa, 1935) are said to be
continuously consumed and released by proton-neutron exchange processes.
Thus, it is concluded that the atom no longer is an ultimate and indivisible particle of matter and the outer or valence shell electrons are responsible for chemical activity of the elements .
But , Bohr theory had to be abandoned because of many short comings. The main objection to Bohr’s theory came from new ideas of De-Broglie and Heisenberg.
dE – BROGLIE’S MATTER WAVES: DUAL NATURE OF MATTER
We have seen that in Bohr`s theory ,the electron is treated as a particle. de-broglie pointed out in 1924 that just as light has both corpuscular and wave properties, an electron also has a dual character i.e.,it can behave as a wave as well as a material particle . This concept of de-broglie was further developed by Schordinger and accordingly moving electrons are considered to have waves of definite wavelength associated with them.
de-Broglie`s Equation
de Broglie deduced a fundamental relation between the wave length of moving particle and its momentum by making use of Einstein’s mass energy relationship and Planck’s quantum theory. The material particle as a wave satisfies the Planck’s relation for a photon, i.e.
E = hν ……….. (1)
where h is Planck’s constant and v is the frequency of the wave. The frequency for light wave, v = C/ λ and for particle wave, v = V/ λ (c = speed of light wave and v = speed of particle wave). At the same time, Einstein’s mass energy relationship is applicable to it, i.e.
E = mc2 (for a photon) ……….. (2)
or E = mv2 (for a particle where v ≠ c) ………….(3)
where m is the mass and v the speed/velocity of the particle. From the equations (1) and (3),
we have
hν = mv 2 ……… (4)
or hν/ λ=mv2
or h/ λ= mv = p (momentum)
or λ=h/p or (h/mv) or p=h/ λ ………(5)
(where momentum p = mv, mass x velocity)
i.e the momentum of the particle (mv) in motion is inversely proportional to wavelength (λ) , Planck`s constant (h)being constant of proportionality . Equation (5) is known as de-broglie`s Equation
According to de-broglie the electron is not a point mass revolving in an orbit it is a standing wave extending around the nucleus in a circular form. If r be the radius of the circle occupied by a wavelength then to justify Bohr’s postulate which states that which states that electrons can move only in those orbits for which the angular momentum is equal to an integral multiple of h/2π i.e. mvr = n.h/2π …………..(6)
This moving electron is considered as a standing wave extended around the nucleus in circular path and not as a mass particle . If the circumference the orbit is an integral multiple of wavelength , λ.
2πr=nλ ……………(7)
fig. An elctron wave extending around the nucleus
It may be recalled that mvr is the angular momentum of the electron which according to eq.(7) is an integral multiple of λ/2π . Therefore the wave mechanical picture presented by de-broglie supports Bohr’s assumption that the angular momentum is an integral multiple of h/2π
Consequence:- From the equation λ=h/mv it is clear that h/mv is negligible for relatively large objects . While with microscopic particle , this quantity can’t be neglected . Thus the particle nature of matter is pre-dominant in describing the properties of relatively large objects where as the wave character s pre-dominant in describing the properties of microscopic particles.
Limitations:- A-The de-broglie eq. is applicable only to microscopic particle such as electrons ,protons , neutrons etc. B- It is not valid for macroscopic particle. C- Wave nature of moving electron was verified by Davison & Germer’s experiment
• Heisenberg Uncertainty Principle :- The dual nature of the electron implies that any precise position cannot be located because a wave is not located at a particular point rather , it extends in space . To describe the character of a subatomic particle that behaves like a wave Werner Heisenberg in 1927 formulated a principle known as Heisenberg’s uncertainty principle . According to this principle,
“it is impossible to determine simultaneously both the position as well as the momentum (or velocity) of a moving particle at the same time with certainty (or accurately)”
∆x.∆p≥ h/4π
∆p=m×∆v
∆x×m×∆v≥h/4π
∆x.∆v≥h/m.4π
Where, ∆x=uncertainty principle
∆p=uncertainty in momentum
∆v=uncertainty in velocity
m=mass of moving particle
Explanation of Heisenberg Uncertainty Principle:- Suppose we attempt to measure both position and momentum of an electron. To locate the position of electron , we have yo use light so that the photon is seen in the microscope. As a result of hitting by the photon the position as well as velocity of the electron are changed. Fig. represents change of momentum & position of electron on impact with a photon .
Application of Heisenberg uncertainty principle
(I)According to this principle
∆x.∆p>h/4π
This equation determines the limit of accuracy about exact measurement of position and momentum of a microscopic particle.
(II) This principle can be used to determine the frequency ‘v’ of radiation emitted by an electron we know
∆x.∆p>h/4π
Now acc. to de-broglie eq. [ν =c/λ => λ=c/ν]
p=h/λ
Δp=h/λ=hΔν/c
hΔν/c.Δx≥h/4π
Δν≥1.c/4π.Δx
(III)From this principle it is clear that electrons cannot exist within the nucleus of an electron (atom).
- Schrodinger`s Wave Equation
To describe the wave motion of electron in hydrogen atom, Schrodinger in 1927 combined the de Broglie’s relation for the wavelength of a particle wave with the well known differential equation for standing waves and proposed a mathematical form called Schrodinger’s wave equation. This equation is now widely used to explain the behaviour of atomic and molecular systems. The equation for a single particle in three dimensional space, i.e. along x, y and z directions is given as follows:
δ2ψ/δx2 + δ2ψ/δy2 + δ2ψ/δz2 + 4π2 ψ/λ2 = o ……….(1)
In place of three partial differentials, symbol ‘∇’ (del) can be used, hence the above equation
becomes
∇2ψ + 4π2 ψ/λ2 = 0 ……….(2)
where ∇2 (del square) is equal to δ2/δx2+ δ2/δy2 + δ2/δz2 and is known as laplacian operator.Putting the value of λ from de Broglie’s relation (i.e. λ = h/mv) the above equation becomes
∇2 ψ +4π2mv2/h2= 0 ……….(3)
Extracting the value of v from kinetic energy, potential energy and total energy terms i.e. E = K.E+V where K.E. = 1/2mv2 and putting in the above equation, we get the final form of the equation as:
∇2 ψ + 8 π2m/h2(E -V) ψ = 0 ……….(4)
This equation is known as Schrodinger’s wave equation.
Significance of ψ and ψ2
An electron, from the probability concept, is considered as a three dimensional wave system extended around the nucleus and is represented by the symbol ψ which denotes the wave function of the electron; ψ itself has no physical significance and simply represents the amplitude of electron wave. Schrodinger’s equation has several solutions for ψ, both real and imaginary. Some of the real values of ψ are appreciable while others are too small and hence neglected. If the value of ψ obtained as above is continuous, finite, single valued and electron probability in space related to ψ is equal to 1, then ψ is known as eigen function (meaning characteristic), ψ2 gives the probability of finding an electron of a given energy, E from place to place in a given region around the nucleus. Since, ψ often contains the imaginary quantity, but the probability of an electron in a given volume must be a real quantity, therefore the product ψ ψ* (ψ star) is used rather than ψ2 where ψ* is complex conjugate of ψ. This product will always be real whereas ψ2 may be real or imaginary. If ψ is real quantity, then ψ and ψ* both are same and hence ψ2 is also a real quantity and corresponds to probability density per unit volume.
Importance of Schrodinger`s wave equation
1-The dual nature of matter is the base of schrodinger wave equation.
2-Schrodinger`s wave equation is the only key to solve the problems of wave mechanics . Schrodinger used this equation in atomic physics and chemistry to solve many problems related to molecules ,atoms,electrons etc.
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