Quantum Mechanical Model Of Atom By-N.K.D. Sir Please -Rate review and share this lesson
QUANTUM MECHANICAL MODEL OF ATOM In 1920, a new model of atom was developed by Ervin Schrodinger. In the atomic model proposed by Schrodinger, idea of quantization and conclusions of de Broglie principle and Heisenberg uncertainty principle were incorporated. In this model the behaviour of the electron in an atom is described by the mathematical equation known as Schrodinger Wave Equation, given below: Here, in this equation, x,y and z are the three space co-ordinates, m = mass of electron, h = Planck's constant, E = total energy, U = Potential energy, wave function of electron wave. The permitted solutions of Schrodinger wave equation are known as wave functions which correspond toa definite energy state of an electron known as orbital. Thus, the discrete Bohr orbits are replaced by orbitals, i.e., "three dimensional region of definite shape about the nucleus where the electron density is maximum or where the probability of finding an electron is maximum or where the electron passes its maximum time." The Schrodinger wave equation may simply be interpreted by stating that a particle or body of mass m, energy E and velocity v possesses wave like properties associated with it, with amplitude given by the wave function (Psi).
ives the three dimensional amplitude of electron wave. 2 dVis the probability o finding an electron in a volume dVabout the nucleus of n tom. The particular wave of w is called eigen function and the value of energy corresponding to this is called eigen value. The eigen function of an electron is called atomic orbital. The wave equation is applicable to atoms as well as molecules. The solution of wave equation gives regions in space where y is +ve as well as-ve . But V (probability of finding an electron) is always positive Distance
Probability Distribution: In wave mechanics, an electron in motion is described by a wave function, -v has no physical significance and refers to the amplitude of the electron wave. However, 2 is a significant term and give the probability of finding an electron or intensity of electron. An atomic orbital is a three dimensional region of definite shape about the nucleus where there is more intensity of electrons An atomic orbital is considered as a diffused electron cloud having more electron density close to the nucleus. The probability of finding an electron in a given volume about the nucleus is understood best in the form of radial probability distribution curves The probability distribution curves for some orbitals are given below. The distance of maximum radial probability is the radius of an atom. The point at which radial probability becomes zero is known as Nodal point. In general there are (n -1) nodal points for s-orbitals; (n -2) for p-orbitals; (n -3) for d-orbitals and (n-4) for f-orbitals (n = principal quantum number).
The radius of maximum probability of 1s electron is 0.53 A (Bohr radius). The number of regions of maximum probability for 1s, 2p, 3d, and 4forbitals are one each. For 2s, 3p, 4d and 5f -atomic orbitals there are two regions of maximum probability. The small humps in the distribution curves show that the electron has a tendency to penetrate closer to the nucleus. In between the regions of maximum electron density, there is a region of zero electrorn density known as nodal point. Greater the number of nodal points, higher is the energy of an orbital.
The solution of Schrodinger wave equation gives the principal (n), azimuthal and magnetic quantum numbers (m) but not the spin quantum number (s). It was introduced on account of the spin of revolving electron. Significance of Quantum Numbers. The four quantum numbers are of physical significance. They give the address of an electron i.e they are capable of indicating the probable position (shell, sub-shell, atomic orbital) and energy of an electron in the atom. For example, if for an electron. n 3,1 = 1, m =-1, and s= +1, then it indicates that the electron is: present in the third shell (M-shell) present in the 3p sub-shell (since for p, 1-1) -present in the 3p, or 3p, atomic orbital spinning in clockwise direction.
Why electron cannot exist inside the nucleus according to Heisenberg's uncertainty principle? Solution Diameter of the atomic nucleus is of the order of 10 m The maximum uncertainty in the position of electron is 10-"m. Mass of electrn91x 10 kg -15 h6.63x104 22 10-15 9.1 10-31 4 Av 5.80x100s This value is much higher than the velocity of light and hence not possible.
Niranjay Kumar Dwivedi
(N.K.D.Sir) is a Complete Chemistry faculty for IIT~JEE, and NEET examination. with more then 8 year of Teaching experience