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. DUAL NATURE OF MATTER • The French physicist, de Broglie in 1924 proposed that matter, like radiation, should also exhibit dual behaviour i.e., both particle and wave like properties. • de Broglie gave the following relation between wavelength (λ) and momentum (p) of a material particle 𝒉 • h λ= • orλ= 𝒎𝒗 p Where, m = mass of electron, v= velocity of electron, λ = wavelength of matter wave associated with electron DUAL NATURE OF MATTER • The de Broglei concept is significant only for microscopic particles not for large object because the wavelengths associated with ordinary objects are so short that their wave properties cannot be detected. • The wavelengths associated with electrons and other subatomic particles (with very small mass) can however be detected experimentally. Nature DUAL Dual NATURE OF MATTER de Broglie Matter has both wave According to Planck’s and particle nature. quantum theory E h (1) According to Einstein’s equation E mc2 Equating (1) and (2) mc2 h c For any particle = (2) mc2 h h mc h mv de Broglie wavelength DUAL NATURE OF MATTER • The wave nature of electron was experimentally proved by Davison & Germer in his X-Ray diffraction experiment Proof:- Quantisation of Angular Momentum Bohr had just invented his “Quantum Hypothesis”, because it explained the Hydrogen-spectrum. He gave no explanation, as to why angular momentum should be “quantized”. 2r n According to de Broglie equation h mv 2r On rearranging we get; nh mvr 2 nh mv Heisenberg’s uncertainty principle it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron. It states that The product of their uncertainties is always equal to or greater than h/4π. Mathematically, 𝒉 Δx.Δp ≥ 𝟒π Where , Δx = uncertainty in measurement of position Δp = uncertainty in measurement of momentum Heisenberg’s uncertainty principle Since Δp = Δ(mv) = m.Δv 𝒉 HenceΔx.mΔv ≥ 𝟒π Or Δx.Δv ≥ 𝒉 𝟒πm Heisenberg’s uncertainty principle rules out the existence of definite paths or trajectories of electrons and other similar particles QUANTUM MECHANICAL MODEL OF THE ATOM • 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 is based on a fundamental equation which is called Schrodinger equation. • Schrodinger’s equation: For a system (such as an atom or a molecule whose energy does not change with time) the Schrödinger equation is written as: QUANTUM MECHANICAL MODEL OF THE ATOM • ψ gives us the amplitude of electron wave. The value of ψ has no physical significance. • Ψ2 gives us the region in which the probability of finding an electron is maximum. It is called probability density. • When Schrödinger equation is solved for hydrogen atom, the solution gives the possible energy levels the electron can occupy and the corresponding wave function(s) of the electron associated with each energy level. Quantum mechanical model of atom • The energy of electrons in atoms is quantised. • The number of possible energy levels for electrons in atoms of different elements is a direct consequence of wave-like properties of electrons. • The position and momentum of an electron cannot be determined simultaneously. • Electrons of different energies are likely to be found in different regions. • The region of space around the nucleus where the probability of finding an electron is maximum is called an atomic orbital. Orbit and Orbital Orbit is a fixed circular path around the nucleus in which electron moves(proposed by Bohr) whereas orbital is the quantum mechanical concept and refers to the wave function. Nodal Plane The plane where the probability of finding the electron is almost zero. Total nodes in a shell = (n -1) Angular nodes = l Spherical nodes= (n –l -1) Quantum Numbers They specify the address (energy & position) of each electron in an atom. These are four types. Quantum Numbers Azimuthal Principal Magnetic Spin Principal Quantum Number (n) • Average distance of the electron from the nucleus • Energy Level of electron • Possible values (n=1,2,3…..) • Maximum number of electrons in any shell is 2n2. Azimuthal or Angular Quantum number:(l) • It identifies sub-shell (sub energy level), the shape of orbitals, and orbital angular momentum. • For a given value of n, l = 0 to n-1 • Total number of subshells in a particular shell is equal to the value of n. s p d f Values of l 0 1 2 3 Subshell Azimuthal or Angular Momentum Quantum number:(l) p s d f Azimuthal or Angular Momentum Quantum Numbers Quantum number:(l) Orbital angular momentum of an electron is given by h l(l 1) 2 Illustrative example The orbital angular momentum of an electron is 4s orbital is 1 h (a) + 4 2p (c) h 2p Solution (b) zero (d) h 4 2p Orbital angular momentum = AIEEE 2003 l l 1 . h 2 For s electrons, l = 0 For 4s electrons, orbital angular momentum is zero. Hence, answer is (b) Magnetic quantum number(m) Magnetic Quantum Number (ml) Orientations of an orbital in space. Explains the Stark and Zeeman effect. Takes (2l+1) values,m=- l to + l. Specifies Orbitals the exact orbital within each sublevel combine to form a spherical shape: 2s 2px 2py 2pz Spin Quantum Number(s) Describes the direction of spin of an electron Clockwise or anticlockwise (+1/2,-1/2) ms = +½ ms = -½ Spin angular momentum= Magnetic moment = h s(s 1) 2 n(n 2) n= no. of unpaired electrons 1 2 Relation between quantum numbers •For every value of n, l = 0 to (n-1) •For every value of l, m = -l to +l •For every value of m, s = 1 2 Quantum Numbers lucknow n Area l Sector House number m s lucknow aliganj J (shell) (sub shell) (orbital) 42 (spin) Pauli’s exclusion principle It is impossible for two electrons in a given atom to have same set of four quantum numbers. For example: In case of 1s2,there are two electrons in the 1s orbital. The quantum numbers of the two electrons are: n=1 , l=0 , m=0 , s=+1/2 n=1 , l=0 , m=0 , s=-1/2 Atomic Orbital Shapes Atomic Orbital Shapes Atomic Orbital Shapes Atomic Orbital Shapes Atomic Orbital Shapes Atomic Orbital Shapes The five d orbitals in ψ(x, y, z)2 form, with a combination diagram showing how they fit together to fill space around an atomic nucleus. Atomic Orbital Shapes Electronic configuration of atoms •Arrangement of electrons in different orbitals of an atom. • The electronic configuration of different atoms can be represented in two ways. a. sapbdc...... notation. b. Orbital diagram:, each orbital of the subshell is represented by a box and the electron is represented by an arrow (↑) a positive spin or an arrow (↓) a negative spin. Aufbau’s principle In the ground state of the atoms, the orbitals are filled in order of their increasing energies . n+l rule Aufbau’s principle 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s Aufbau’s principle For example: Consider 3d and 4s orbitals, the electron will first enter the orbital having minimum value of (n+l). Electron will therefore enter 4s orbital (4+0=4) before entering 3d orbital (3+2=5). Aufbau’s principle Incase (n+l) values are same!!! Incase of 3d orbital (3+2=5) and 4p orbital (4+1=5), the (n+l) values are same. In such a case,electron enters the orbital for which n is minimum. The electron will thus enter 3d orbital before entering 4p orbital. Hund’s rule •The most stable arrangement of electrons in sub shells is the one with the greatest number of parallel spins. •Electron pairing starts only after all the degenerate orbitals are filled with electrons having same direction of spin. For example: Nitrogen (Atomic number=7) Electronic configuration 1s2 2s2 2p3 Degenerate refers to orbitals having same energy. Electronic configuration some elements Electronic configuration some elements Electronic configuration some elements Exceptional electronic configuration Orbitals in the same sub shell tend to become completely filled or half filled since such orbitals are more stable. Such as electronic configuration of Cr(24): [Ar]3d44s2 But actually it is [Ar]3d54s1 electronic configuration of Cr(24): [Ar]3d44s2 But actually it is [Ar]3d54s1 Thank you