19.1 Atomic Physics. IIQuantum numbersPauli Exclusion PrinciplePeriodic TableCharacteristic x-raysElectrons in atoms.Electrons in atoms exist in discrete energy levels which can be calculated by solving a wave equation. This calculation is beyond the scope of this course. However, the pattern of energy levels which results from a quantum mechanical rule called the Pauli Exclusion Principle. is responsible for the periodicity in the chemical properties of the different elements as seen in the Periodic Table.Bohr atomn=1n=2n=3Quantum mechanics2 states8 states18 statesQuantum calculations show that more statesare needed to describe the electrons in an atom2262610The number of states determinedby quantum numbers.Orbital angular momentumClassically the angular momentum L of an electron movingin a circle can have any valuevrmIn quantum mechanics thevalues of the angular momentum are quantized and specified by a orbital angular momentum quantum no. ℓFor an electron with a principle quantum no. n the value of ℓ ranges from 0 to n-1.Li.e. for n=2 , ℓ can have values of 0 and 1.Orbital magnetic quantum numberMagnetic fieldLClassically an electron moving in a circle is a currentwhich results in a magnetic dipole.Classically, the dipole can have any orientation withrespect to a field.In quantum mechanics, only discrete orientations areallowed. The orientation are determined by the orbitalmagnetic quantum no. ml The value of ml ranges from – ℓ to + ℓ.ml=1ml=0ml=-1. ℓ =1i.e. for ℓ=1, ml can have values of -1, 0, and 1.Spin magnetic quantum numberIn quantum mechanics an electron has an intrinsicmagnetic moment due to spin. The magneticmoment can have two orientations in a magnetic field determined by a spin quantum number mse-sms=1/2ms= - 1/2ms = +1/2 or -1/2for an electron 2 spin states are possible +1/22Atomic energy levels and quantum numbers.principle quantum number nangular momentum quantum numberorbital magnetic quantum number m range of values1, 2, 3, ...........A0, 1 to n-1A,..to..−+AAspin magnetic quantum number ms11,or22−+The state of an electron is specified by the set of its quantumnumbers (n, ℓ, ml ,, ms)The number of states is determined by the set of possiblequantum numbers.2+½1232+½2232+½0232+½-1232+½-2232+½1132+½0132+½-1132+½0032+½1122+½0122+½-1122+½0022+½001no. ofstatesmsmllnElectronic states in an atom n=1,2 and 3no. n28182262610no. n, lPauli Exclusion PrincipleNo two electrons in an atom can have the same quantumnumber, n, l, ml , or ms.To form an atom with many electrons the electronsgo into the lowest energy unoccupied state.The periodic properties of the elements as shown in thePeriodic Table can be explained by the Pauli ExclusionPrinciple by properties of filled shells.Electrons in atoms- Shell NotationPeriodic Table of the ElementsDmitri Mendeleev (1834-1907)noblegases21018365486Z3Noble gas configurationsHe Z= 2 1s2Ne Z=10 1s22s22p6Ar Z=18 1s2 2s22p63s23p6Kr Z= 36 1s2 2s22p63s23p64s24p63d10Noble gases have Filled SubshellsFilled subshell configuration s2, p6, d10Noble gases have filled subshellsStable, difficult to ionize A -> A+ +
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