Atomic Theory Lecture 2 PDF

PL1001 Pharmaceutical Chemistry ATOMIC THEORY Lecture 2 Dr Alberto Di Salvo Electron vs Golf ball The wavelength of a moving body is inversely proportional to its momentum. momentum = mass (kg) x velocity (m/s) L...

PL1001 Pharmaceutical Chemistry ATOMIC THEORY Lecture 2 Dr Alberto Di Salvo Electron vs Golf ball The wavelength of a moving body is inversely proportional to its momentum. momentum = mass (kg) x velocity (m/s) Louis de Broglie Property Electron Golf ball h Mass (kg) 9.11x10-31 0.01 𝜆= 𝑚𝑣 Velocity (m/s) 100 100 Momentum (kg m/s) 9.11x10-29 1 Wavelength (m) 7.27x10-6 6.626x10-34 h= Planck’s constant Large λ Small λ (6.626 x 10-34 J s) Mechanics theory Quantum Classical The motion of large bodies is better described by classical mechanics, while the motion of particles is better described by quantum mechanics. Energy quantisation E E == hh ·· The relationship between the temperature of a black body and the intensity of energy it emits as radiation follows a stepwise relationship. Each of these steps is called quantum. Photoelectric effect E E == nh nh Classical theory stated that E of ejected electron should steadily increase with an increase in light intensity (not observed!) No e- is ejected until light of a certain minimum E is used. Albert Einstein Number of e- ejected (n) depends on light intensity.  Quantum or Wave Mechanics Schrödinger applied the idea of electrons behaving as a wave to the problem of electrons in atoms. He developed the WAVE EQUATION Erwin Schrödinger Solution of the wave equation gives a set of mathematical expressions called WAVE FUNCTIONS,   Uncertainty Principle Problem of defining energy and position of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (= m v) or energy of an electron. Chemists define e- energy exactly Werner Heisenberg but accept the limitation that the exact position of such e- is not known.  Born’s Interpretation  does NOT describe the exact location of an electron. 2 is proportional to the probability of finding an electron in a portion of space identified by certain quantum numbers. Max Born Wave motion: wave length and nodes  QUANTUM NUMBERS Not all wave functions are valid solutions of Schrödinger’s wave equation. (It has been proven experimentally that) Electrons’ energy levels are quantised. Quantum numbers are spatial “constraints” (limit areas) where wave functions are valid and there is a high probability of finding electrons.  Shells and subshells Quantum numbers identify shells (limit areas) and subshells Subshells are grouped in shells. Each shell is associated to a number called the PRINCIPAL QUANTUM NUMBER, n The principal quantum number of the shell is the number of the period or row of the periodic table where that shell begins being filled with electrons.  Shells and subshells n=1 n=2 n=3 n=4  QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 3 quantum numbers: n (principal) shell l (angular) subshell ml (magnetic) identifies an orbital within a subshell Quantum Numbers (QN) Principal QN: n = 1, 2, 3, 4…… Shorthand notation for orbitals Rule: l = 0, s orbital; Angular momentum QN: l = 1, p orbital; l = 2, d orbital l = 0, 1, 2, 3…. (n -1) l = 3, f orbital Rule: l (n - 1) 1s, 2s, 2p, 3s, 3p, 4s, 4p, 4d, etc. Magnetic QN: ml = …-2, -1, 0, 1, 2,.. Rule: -l ml +l The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of n shell = all orbitals with the same value of n subshell = all orbitals with the same value of n and l an orbital is fully defined by three quantum numbers, n, l, and ml Each shell of QN = n contains n subshells n = 1, one subshell n= 2, two subshells, etc Each subshell of QN = l, contains 2l + 1 orbitals l = 0, 2(0) + 1 = 1 l = 1, 2(1) + 1 = 3  The fourth quantum number: Electron Spin ms = +1/2 (spin up) or -1/2 (spin down) Spin is a fundamental property of electrons, like its charge and mass. (spin up) (spin down)  QUANTUM NUMBERS, ORBITALS AND ELECTRONS Electrons in an orbital must have different values of ms This statement demands that if there are two electrons in an orbital one must have ms = +1/2 (spin up) and the other must have ms = -1/2 (spin down). This is the Pauli Exclusion Principle An empty orbital is fully described by the three quantum numbers: n, l and ml An electron in an orbital is fully described by the four quantum numbers: n, l, m and m