(i) Azimuthal quantum number is also known as angular quantum number. (viii) Angular momentum can also be calculated using principle quantum number. (vii) It represents the major energy shell or orbit to which the electron belongs. (vi) The value of energy increases with the increasing value of n. (v) It gives the information of orbit K, L, M, N. (iv) The maximum number of an electron in an orbit represented by this quantum number as 2n 2 No energy shell in atoms of known elements possess more than 32 electrons. (iii) It determine the energy of the electron in an orbit where electron is present. (ii) It determines the average distance between electron and nucleus, means it is denoted the size of atom. (i) It was proposed by Bohr’s and denoted by ‘ n’. (1) Each orbital in an atom is specified by a set of three quantum numbers ( n, l, m) and each electron is designated by a set of four quantum numbers ( n, l, m and s). (iv) The solution of this equation provides a set of number called quantum numbers which describe specific or definite energy state of the electron in atom and information about the shapes and orientations of the most probable distribution of electrons around the nucleus. And the place where probability of finding is maximum is called electron density, electron cloud or an atomic orbital. (iii) If Ψ 2 is maximum than probability of finding e − is maximum around nucleus. (ii) For a single particle, the square of the wave function Ψ 2 at any point is proportional to the probability of finding the particle at that point. The amplitude Ψ is thus a function of space co-ordinates and time i.e. Ψ = Ψ (x, y, z…………times) (i) The wave function Ψ represents the amplitude of the electron wave. (4) The Schrodinger wave equation can also be written as : Where x, y and z are the 3 space co-ordinates, m = mass of electron, h = Planck’s constant,Į = Total energy, V = potential energy of electron, = amplitude of wave also called as wave function. (3) The probability of finding an electron at any point around the nucleus can be determined by the help of Schrodinger wave equation which is, (2) In it electron is described as a three dimensional wave in the electric field of a positively charged nucleus. the equivalent mass a point located at the centre of gravity of the system would have: μ = m + M m M , where M is the mass of the nucleus and m the mass of the electron.(1) Schrodinger wave equation is given by Erwin Schrödinger in 1926 and based on dual nature of electron. With the system consisting of two masses, we can define the reduced mass, i.e. The potential, V between two charges is best described by a Coulomb term,V(r)= 4 π ϵ r − Z e 2 where Ze is the charge of the nucleus ( Z=1 being the hydrogen case, Z=2 helium, etc.), the other e is the charge of the single electron, ϵ is the permittivity of vacuum (no relative permittivity is needed as the space inside the atom is "empty"). We'll see later how we can use the exact solution for the hydrogen-like atom as an approximation for multi-electron atoms. Nucleus can be bigger than just a single proton, though. A hydrogen-like atom is an atom consisting of a nucleus and just one electron the Application of Schrodinger wave equation to hydrogen atom To fill the Schrdinger equation, H ψ = E ψ with a bit of life, we need to add the specifics for the system of interest, here the hydrogen-like atom.
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