The behavior of electron in the atom which have been observed after Bohr's atomic model are mentioned here as follows:
* the complication in the origin of atomic spectra along with the existence of discrete nature of radiant energy of an atomic system.
* the evidence of wave-particle duality of electron and development of de-Broglie equation.
* uncertainty of determination of position of electron in an atom based on Heisenberg's uncertainty of determination of position of electron in an atom based on Heisenberg's uncertainty principle.
These observation make the behavior of electron of an atom more complicated. Bohr's atomic model proposed on the basis of classical quantum theory of radiation was unable explain all about the behavior of electron. It was in need of a conceptual atomic model. Keeping all these observation in mind Erwin Schrodinger in 1926 developed a new quantum or wave mechanical model of atom and invented a method of showing how to the properties of waves could be used to explain the behavior of electron in atom.
Wave Particles Duality: de Broglie equation
The Bohr's model of atom with electron as discrete particles with precisely defined positions and velocities has in recent year been modified by assuming the wave nature of electron. Though photoelectric effect is the evidence for the particles nature of electron yet, diffraction pattern obtained by Clinton Davisson and Lester Germer by passing a beam of electron on nickel crystal is the evidence for wave nature of electron i.e., an electron has dual character, particle and wave but it cannot at the same time behave as both.
According to quantum theory of radiation, the energy of a photon is equal to hv and Einstein's equivalence of mass and energy it follows that hv=mc2 , where m is the mass equivalent of the given photon, v= frequency of photon and c= speed of photon.
Combining E=hv and E=mc2
or. hv=mc2
or, h(c/λ)=mc2
or, mc=h/λ
Hence, momentum of photon(p)=h/λ,
This equation can be applied not only for photon but also to any moving particles as:
λ=h/(mv) where λ= De Broglie wavelength associated with a particles of mass m moving with a velocity v and the equation is called de-Broglie equation after the name of French physicist Louis De Broglie.
Significance of the equation
i. The equation tells that every moving particles associates wave as well as particles nature. It has been calculated from the equations that wavelength associated with a macro particles is too small to be detected and it is neglected whereas in the case of micro particles e.g., electron the wavelength so calculated is appreciable and it is also detected as electron diffraction pattern. Hence, electron possesses appreciable wave nature besides its particles nature.
ii. de Broglie, considering dual nature of electron proposed different close orbit around the nucleus similar to Bohr's atomic model for standing electron wave. Here the circumference of allowed orbit is integral multiple of the wavelength of electron accommodate one, two and three complete wavelength of electron respectively so that electron wave suffers neither constructive nor destructive interferences.
The circumference of orbit (2πr) = n×λ
=nλ
According to de Broglie equation
2πr = n × (h/mv)
mvr = nh/2π
This equation is in close agreement with bohr's theory of quantization of angular momentum. That such proposal of atomic model is also not found to be in consistent with uncertainty principle.
Heisenberg's Uncertainty Principle
A German scientist Warner Heisenberg in 1927 concluded from the existence of dual nature of electron that the measurement of the position and momentum of an electron cannot be made simultaneously. This principle is known as Heisenberg's Uncertainty Principle.
Statement: It is impossible to measure simultaneously the exact position and exact velocity or momentum of a sub-atomic particles like electron, neutron and other Quantum particles.
Classical mechanics defines a thing as a particles only when its position and momentum or velocity is determined precisely at a time and it is possible for macroscopic (large) particles such as bullet, tennis ball etc. but for microscopic particles such as electron, such precise measurement of position and velocity is impossible due to the effect of wave-particle duality. Here, the more precisely we determine the position of electron, the less we know about its motion or momentum.
In order to determine the position of an electron present in an atom, light having wavelength comparable to the size of electron is required and for this purpose x-ray, the electron undergoes Compton's recoil so that its velocity or momentum becomes quite uncertain and vice-versa.
In order to deal with the behavior of microscopic particle, Heisenberg introduced a relation in which the product: uncertainty of position (Δx) × uncertainty of momentum (Δp) ≥ h/(4π) ≈ h.
Consider an electron moving with certain velocity around the nucleus of an atom and here uncertainty of momentum (ΔP) = 0 and there by the uncertainty of position of the electron Δx=∞., When the velocity of an electron is defined, the position of that electron at the instant becomes undefined and vice-versa. This is Heisenberg's uncertainty principle and it is the fundamental principle of natural science.
Significance of the Principle
i) The concept of atomic model as proposed earlier is not to be in consistent with the recognition of uncertainty principle. The impossibility of determination of exact path of electron moving with certain velocity makes well defined electron orbits proposed by Bohr's atomic theory inaccurate i.e.., Bohr's atomic model appears to be defective in the light of Heisenberg's uncertainty principle.
ii) Based upon uncertainty principle, it is impossible to determine the xact position of electron moving with certain velocity around the nucleus and keeping the aspect of the principle in mind, Heisenberg's introduced the concept of probability to describe the position of electron in the atom which led to the concept of orbital.
Concept of probability
Experimental evidences and de-Broglie matter-wave concept concluded that an electron as a particle behaves appreciably as wave and it remains in atom as a standing wave. On the other side, Heisenberg uncertainty principle explains the impossibility of measurement of exact position of electron in an atom, Heisenberg introduced the concept of statistical mechanics which is the concept of probability.
Suppose, the intensity of electron wave to find at every point of atomic domains is measured and if the intensities of all points so measured are compiled a picture for the distribution of electron as a cloud is obtained which is the region converging three dimensional space. This region outside the nucleus of an atom where there is maximum probability of finding electron in terms as an atomic orbital. The revolving electron of an nucleus of an atom the momentum at that instant basis of uncertainty principle and therefore there is no probability of finding the electron in the nucleus. Hence, The region in atom where there is maximum probability of finding electron is called the atomic orbital. The nucleus is at the Centre of an atom having no probability of finding electron and it is a nodal Centre for each atomic orbital.
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