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General Physics (PHY 2140)
Lecture 35Lecture 35
Modern Physics
Atomic PhysicsThe periodic tableAtomic transitions
Chapter 28
http://www.physics.wayne.edu/~apetrov/PHY2140/
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Lightning ReviewLightning Review
Last lecture:
1.1. Atomic physicsAtomic physics De Broglie waves/hydrogen atomDe Broglie waves/hydrogen atom Quantum mechanics and spinQuantum mechanics and spin
Review Problem: An emission spectrum for hydrogen can be obtained by analyzing the light from hydrogen gas that has been heated to very high temperatures (the heating populates many of the excited states of hydrogen). An absorption spectrum can be obtained by passing light from a broadband incandescent source through hydrogen gas. If the absorption spectrum is obtained at room temperature, when all atoms are in the ground state, the absorption spectrum will
1. be identical to the emission spectrum.2. contain some, but not all, of the lines appearing in the emission spectrum.3. contain all the lines seen in the emission spectrum, plus additional lines.4. look nothing like the emission spectrum.
2 , 1, 2,3,...r n n
, 1, 2,3,...em vr n n
2 2
1 1 1H
f i
Rn n
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Quantum Number SummaryQuantum Number Summary
The values of n can increase from 1 in The values of n can increase from 1 in integerinteger steps stepsThe values of The values of ℓ can range from 0 to n-1 in integer stepsℓ can range from 0 to n-1 in integer stepsThe values of The values of mm ℓℓ can range from -ℓ to ℓ in integer steps can range from -ℓ to ℓ in integer steps
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28.9 The Pauli Exclusion Principle28.9 The Pauli Exclusion Principle
Recall Bohr’s model of an atom. Why don’t all the Recall Bohr’s model of an atom. Why don’t all the electrons stay on the lowest possible orbit?electrons stay on the lowest possible orbit?
Pauli’s exclusion principle:Pauli’s exclusion principle: no two electrons in an atom no two electrons in an atom can ever be in the same quantum statecan ever be in the same quantum state
In other words, no two electrons in the same atom can have In other words, no two electrons in the same atom can have exactly the same values for n, exactly the same values for n, ℓ, ℓ, mm ℓℓ, and m, and mss
This explains the electronic structure of complex atoms This explains the electronic structure of complex atoms as a as a successionsuccession of filled energy levels with different of filled energy levels with different quantum numbersquantum numbers
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ExamplesExamples
1.1. Hydrogen (one electron), 1sHydrogen (one electron), 1s11
2.2. Helium (two electrons), 1sHelium (two electrons), 1s22
3.3. Lithium (three electrons), 1sLithium (three electrons), 1s222s2s11
1, 0, 0, 1sn m m
1, 0, 0, 1 21, 0, 0, 1 2
s
s
n m mn m m
1, 0, 0, 1 21, 0, 0, 1 22, 0, 0, 1 2
s
s
s
n m mn m mn m m
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The Periodic TableThe Periodic Table
The outermost electrons are The outermost electrons are primarily responsible for the primarily responsible for the chemical properties of the chemical properties of the atomatomMendeleev arranged the Mendeleev arranged the elements according to their elements according to their atomic masses and chemical atomic masses and chemical similaritiessimilaritiesThe electronic configuration The electronic configuration of the elements explained by of the elements explained by quantum numbers and quantum numbers and Pauli’s Exclusion Principle Pauli’s Exclusion Principle explains the configurationexplains the configuration
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Bit of history: Mendeleev’s original tableBit of history: Mendeleev’s original table
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Problem: electron configuration of OProblem: electron configuration of O
(a) Write out the electronic configuration of the ground state (a) Write out the electronic configuration of the ground state for oxygen (for oxygen (Z Z = 8). (b) Write out values for the set of = 8). (b) Write out values for the set of quantum numbers quantum numbers nn, , ll, , mmll,, and and mmss for each of the for each of the electrons in oxygen.electrons in oxygen.
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(a) Write out the electronic configuration of the ground state for oxygen ((a) Write out the electronic configuration of the ground state for oxygen (Z Z = 8). (b) = 8). (b) Write out values for the set of quantum numbers Write out values for the set of quantum numbers nn, , ll, , mmll,, and and mmss for each of the for each of the electrons in oxygen.electrons in oxygen.
Given:
Z = 8
Find:
structure
Recall that the number of electrons is the same as the charge of the nucleus. Thus, we have 8 electrons.
1, 0, 0, 1 22, 0, 0, 1 22, 1, (0,1), 1 2
s
s
s
n m mn m mn m m
Thus, electron configuration is2 2 41 2 2s s p
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QUICK QUIZ
Krypton (atomic number 36) has how many electrons in its next Krypton (atomic number 36) has how many electrons in its next to outer shell (to outer shell (n n = 3)?= 3)?
(a) 2(a) 2 (b) 4(b) 4(c) 8(c) 8 (d) 18(d) 18
(d). Krypton has a closed configuration consisting of filled (d). Krypton has a closed configuration consisting of filled nn=1, =1, nn=2, =2, and and nn=3 shells as well as filled 4=3 shells as well as filled 4s s and 4and 4p p subshells. The filled subshells. The filled nn=3 =3 shell (the next to outer shell in Krypton) has a total of 18 electrons, 2 shell (the next to outer shell in Krypton) has a total of 18 electrons, 2 in the 3in the 3s s subshell, 6 in the 3subshell, 6 in the 3p p subshell and 10 in the 3subshell and 10 in the 3d d subshell.subshell.
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Characteristic X-RaysCharacteristic X-Rays
When a metal target is When a metal target is bombarded by high-energy bombarded by high-energy electrons, x-rays are emittedelectrons, x-rays are emittedThe x-ray spectrum typically The x-ray spectrum typically consists of a broad continuous consists of a broad continuous spectrum spectrum and a series of sharp and a series of sharp lineslines
The lines are dependent on The lines are dependent on the metalthe metal
The lines are called The lines are called characteristic x-rayscharacteristic x-rays
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Explanation of Characteristic X-RaysExplanation of Characteristic X-Rays
The details of atomic structure can be used to explain The details of atomic structure can be used to explain characteristic x-rayscharacteristic x-rays
A bombarding electron collides with an electron in the target A bombarding electron collides with an electron in the target metal that is in an inner shellmetal that is in an inner shell
If there is sufficient energy, the electron is removed from the If there is sufficient energy, the electron is removed from the target atomtarget atom
The vacancy created by the lost electron is filled by an electron The vacancy created by the lost electron is filled by an electron falling to the vacancy from a higher energy levelfalling to the vacancy from a higher energy level
The transition is accompanied by the emission of a photon The transition is accompanied by the emission of a photon whose energy is equal to the difference between the two levelswhose energy is equal to the difference between the two levels
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Moseley PlotMoseley Plot
λ is the wavelength of the Kλ is the wavelength of the K lineline
KK is the line that is is the line that is produced by an electron produced by an electron falling from the L shell to falling from the L shell to the K shellthe K shell
From this plot, Moseley was From this plot, Moseley was able to determine the Z values able to determine the Z values of other elements and produce of other elements and produce a periodic chart in excellent a periodic chart in excellent agreement with the known agreement with the known chemical properties of the chemical properties of the elementselements
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Atomic Transitions – Energy LevelsAtomic Transitions – Energy Levels
An atom may have many An atom may have many possible energy levelspossible energy levelsAt ordinary temperatures, most At ordinary temperatures, most of the atoms in a sample are in of the atoms in a sample are in the ground statethe ground stateOnly photons with energies Only photons with energies corresponding to differences corresponding to differences between energy levels can be between energy levels can be absorbedabsorbed
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Atomic Transitions – Stimulated AbsorptionAtomic Transitions – Stimulated Absorption
The blue dots represent The blue dots represent electronselectronsWhen a photon with energy When a photon with energy ΔE is absorbed, one electron ΔE is absorbed, one electron jumps to a higher energy jumps to a higher energy levellevel
These higher levels are These higher levels are called called excited statesexcited states
ΔE = hƒ = EΔE = hƒ = E22 – E – E11 In general, ΔE can be the In general, ΔE can be the
difference between any two difference between any two energy levelsenergy levels
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Atomic Transitions – Spontaneous EmissionAtomic Transitions – Spontaneous Emission
Once an atom is in an excited Once an atom is in an excited state, there is a constant state, there is a constant probability that it will jump back probability that it will jump back to a lower state by emitting a to a lower state by emitting a photonphotonThis process is called This process is called spontaneous emissionspontaneous emission
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Atomic Transitions – Stimulated EmissionAtomic Transitions – Stimulated Emission
An atom is in an excited stated An atom is in an excited stated and a photon is incident on itand a photon is incident on itThe incoming photon The incoming photon increases the probability that increases the probability that the excited atom will return to the excited atom will return to the ground statethe ground stateThere are two emitted There are two emitted photons, the incident one and photons, the incident one and the emitted onethe emitted one
The emitted photon is in The emitted photon is in exactly in phase with the exactly in phase with the incident photonincident photon
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Population InversionPopulation Inversion
When light is incident on a system of atoms, both stimulated When light is incident on a system of atoms, both stimulated absorption and stimulated emission are equally probableabsorption and stimulated emission are equally probableGenerally, a net absorption occurs since most atoms are in the Generally, a net absorption occurs since most atoms are in the ground stateground stateIf you can cause more atoms to be in excited states, a net emission If you can cause more atoms to be in excited states, a net emission of photons can resultof photons can result
This situation is called a This situation is called a population inversionpopulation inversion
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LasersLasers
To achieve laser action, three conditions must be metTo achieve laser action, three conditions must be met
The system must be in a state of population inversionThe system must be in a state of population inversion The excited state of the system must be a The excited state of the system must be a metastable statemetastable state
Its lifetime must be long compared to the normal lifetime of Its lifetime must be long compared to the normal lifetime of an excited statean excited state
The emitted photons must be confined in the system long The emitted photons must be confined in the system long enough to allow them to stimulate further emission from other enough to allow them to stimulate further emission from other excited atomsexcited atoms
This is achieved by using reflecting mirrorsThis is achieved by using reflecting mirrors
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Production of a Laser BeamProduction of a Laser Beam
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Laser Beam – He Ne ExampleLaser Beam – He Ne Example
The energy level diagram for NeThe energy level diagram for NeThe mixture of helium and neon is The mixture of helium and neon is confined to a glass tube sealed at confined to a glass tube sealed at the ends by mirrorsthe ends by mirrorsA high voltage applied causes A high voltage applied causes electrons to sweep through the electrons to sweep through the tube, producing excited statestube, producing excited statesWhen the electron falls to EWhen the electron falls to E22 in in Ne, a 632.8 nm photon is emittedNe, a 632.8 nm photon is emitted
