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CBSE Class XI Chemistry :- Structure Of Atom :- Quantum mechanical model of atom

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- 1. Made by :- Name :- Pranav Ghildiyal Class :- XI B
- 2. Classical mechanics, based on Newton’s laws of motion, successfully describes the motion of all macroscopic which have essentially a particle-like behaviour However it fails when applied to microscopic objects like electrons, atoms, molecules etc. This is mainly because of the fact that classical mechanics ignores the concept of dual behaviour of matter especially for sub-atomic particles and the uncertainty principle. The branch of science that takes into account this dual behaviourof matter is called quantum mechanics. Quantum mechanics is a theoretical science that deals with the study of the motions of the microscopic objects that have both observable wave like and particle like properties. Quantum mechanics was developed independently in 1926 by Werner Heisenberg and Erwin Schrödinger. The fundamental equation of quantum mechanics was developed by Schrödinger and it won him the Nobel Prize in Physics in 1933. This equation which incorporates waveparticle duality of matter was proposed by de Broglie
- 3. Types of Quantum NumbersTypes of Quantum Numbers
- 4. The principal quantum number ‘n’ is a positive integer with value of n = 1,2,3... .The principal quantum number determines the size and to large extent the energy of the orbital. For hydrogen atom and hydrogen like species (He + , Li, .... etc.) energy and size of the orbital depends only on ‘n’. The principal quantum number also identifies the shell.the increase in the value of ‘n’, the number of allowed orbital increases and are given by the following letters . n = 1 2 3 4 Shell = K L M N .
- 5. Size of an orbital increases with increaseofSize of an orbital increases with increaseof principalprincipal quantum number ‘quantum number ‘n’.n’. Each shell consists of one orEach shell consists of one or moremore sub-shellsor sub-levels. The number of sub-shellsinsub-shellsor sub-levels. The number of sub-shellsin aa principal shell is equal to the value value of n.Forprincipal shell is equal to the value value of n.For example in the first shell (example in the first shell ( nn = 1), there is only one= 1), there is only one sub-sub- shell which corresponds l = 0. Each sub-shell isshell which corresponds l = 0. Each sub-shell is assigned an azimuthal quantum number. Sub-shellsassigned an azimuthal quantum number. Sub-shells corresponding to different values ofcorresponding to different values of ll areare representedrepresented in the following tablein the following table Value for l 012345........... . notation for sub- shell spdf gh............
- 6. n L SubShell notations 1 0 1s 2 0 2s 2 1 2p 3 0 3s 3 1 3p 3 2 3d 4 0 4s 4 1 4p 4 2 4d 4 3 4f
- 7. Magnetic orbital quantum number. ‘m’ gives information about the spatial orientation ofMagnetic orbital quantum number. ‘m’ gives information about the spatial orientation of thethe orbital with respect to standard set of co-ordinate axis. For any sub-shell (defined by ‘l’orbital with respect to standard set of co-ordinate axis. For any sub-shell (defined by ‘l’ value)value) 2l+1 values of m are possible and these values are given by : m2l+1 values of m are possible and these values are given by : m11 = – l, – (l –1), – (l –2)... 0,1...= – l, – (l –1), – (l –2)... 0,1... (l – 2), (l–1), l.(l – 2), (l–1), l. for l = 0, the only permitted value of mfor l = 0, the only permitted value of mll = 0, [2(0)+1 = 1, one s orbital]. For can be –1, 0 and= 0, [2(0)+1 = 1, one s orbital]. For can be –1, 0 and +1 [2(1)+1 = 3, three orbitals]. For l = 2, m = –2, –1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals]. It+1 [2(1)+1 = 3, three orbitals]. For l = 2, m = –2, –1, 0, +1 and +2, [2(2)+1 = 5, five d orbitals]. It should be noted that the values of mshould be noted that the values of mll are derived from that the value of l are derived fromare derived from that the value of l are derived from n.n. Value of l 0 1 2 3 4 5 Subshell notation s p d f g h number of orbitals 1 3 5 7 9 11
- 8. In 1925, George Uhlenbeck and Sameul Goudsmit proposed theIn 1925, George Uhlenbeck and Sameul Goudsmit proposed the presense of the fourth quantum number known as electron spinpresense of the fourth quantum number known as electron spin quantum number. An electron spins around its own axis, much inquantum number. An electron spins around its own axis, much in aa Similar way as earth spins around its own axis while revolvingSimilar way as earth spins around its own axis while revolving aroundaround the sun. Spin angular momentum of the electron — a vectorthe sun. Spin angular momentum of the electron — a vector quantity,quantity, can have two orientations relative to the chosen axis. These arecan have two orientations relative to the chosen axis. These are the twothe two spin states of the electron and are normally represented by twospin states of the electron and are normally represented by two arrows, ↑ (spin up) and ↓ (spin down). Two electrons that havearrows, ↑ (spin up) and ↓ (spin down). Two electrons that have differentdifferent mm values (one+ and the other –) are said to havevalues (one+ and the other –) are said to have oppositeopposite spins. An orbital cannot hold more than two electrons and thesespins. An orbital cannot hold more than two electrons and these twotwo
- 9. ‘‘n’ defines the shell, determines the size of the orbital and alson’ defines the shell, determines the size of the orbital and also to ato a large extent the energy of the orbitallarge extent the energy of the orbital There areThere are n subshells in then subshells in the nnthth shell, ‘l’ identifies the subshellshell, ‘l’ identifies the subshell andand determines theshape of the orbital.There are (2determines theshape of the orbital.There are (2 l+1) orbitals ofl+1) orbitals of eacheach type in atype in a subshell, that is,onesubshell, that is,one s orbital (l = 0), Three p orbitals (l =s orbital (l = 0), Three p orbitals (l = 1)1) and five d orbitals (l = 2)and five d orbitals (l = 2) per subshell. To some extent ‘per subshell. To some extent ‘ l’ alsol’ also determines the energy of the orbital in a multi-electron atom.determines the energy of the orbital in a multi-electron atom. MMll designates the orientation of the orbital. For a given value ofdesignates the orientation of the orbital. For a given value of l,l, mm has (2has (2l+1)l+1) values, the same as the number of orbitals pervalues, the same as the number of orbitals per
- 10. The orbital wave function or ψ for an electron in an atom has no physical meaning. It is simply a mathematical function of the coordinates of the electron. However, for different orbitals the plots of corresponding wave functions as a function of r (the distance from the nucleus) are different According to the German physicist, Max Born, the square of the wave function (ψ2 ) at a point gives the probability density of the electron at that point. For 1s orbital the probability density is maximum at the nucleus and it decreases sharply as we move
- 11. 1s {n=1, l= 0 } 2s {n=2, l=0} 1s orbitals 2s orbitals
- 12. For 2p orbitals For 2p orbitals For 3d orbitals For 3d orbitals
- 13. The filling of electrons into the orbitals of different atoms takes place according to the aufbau principle which is based on the Pauli’s exclusion principle, the Hund’s rule Of maximum multiplicity and the relative energies of the orbitals.
- 14. The distribution of electrons into orbitals of an atom is called its electronic configuration. If one keeps in mind the basic rules which govern the filling of different atomic orbitals, the electronic configurations of different atoms can be written very easily.

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