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© Prof. Zvi C. Koren1 19.07.10
The Electronic Structure of the Atom:
Historical Background
Fireworks
:7נושא
:המבנה האלקטרוני של האטוםרקע היסטורי
movie
© Prof. Zvi C. Koren2 19.07.10
Rutherford
Millikan
Maxwell
Thomson
Einstein
Heisenberg
SchrödingerBohr
Balmer
Planck
Rydberg
de BroglieBorn
© Prof. Zvi C. Koren3 19.07.10
Sir Joseph John (J.J.) Thomson
Conclusions:
1. Cathode ray particles (“corpuscles”) are negatively charged
2. Calculated the charge-to-mass ratio, e/m, of this particle
(“electron”) from the electric and magnetic forces:
e/m = 1.76 x 108 C/g. (C = Coulomb, קולון)
3. This e/m ratio is independent of:
(a) the cathode material; (b) the residual gas in tube.
Experiment: Cathode Ray Tube, 1897
Electric field only
Electric + Magnetic fieldsCathode
Anode
1856 – 1940, England
Nobel Prize in Physics, 1906
George Johnstone Stoney1826 – 1911, Ireland
Coined the name “electron”in 1874
Conclusion: Calculated e/m, Charge-to-Mass Ratio of e–
e–
© Prof. Zvi C. Koren4 19.07.10
(note the raisins)
Where Are the Electrons in the Atom – According to J.J. Thomson?
The Famous
Plum Pudding (with Raisins) Model
1890’s
The Thomson Atom
with e’s dispersed
within a
homogeneous
positive (+) sphere
© Prof. Zvi C. Koren5 19.07.10
Robert Andrews Millikan
Experiment: Oil Drop, 1909
1868 – 1953, USA
Nobel Prize in Physics, 1923
Conclusion: Calculated e, the Charge on an e–
Conclusions:
1. Each q is a multiple of a basic charge: q = n·e
2. The basic charge is therefore that for the electron: e = 1.60 x 10–19 C.3. Thus, the mass m of an electron can be calculated together with Thomson’s result for e/m:
m = 9.11 x 10–28 g.
Equatinggravitational force with
electrical force allows for the calculations of the
charges, q, on the oil drops (in units of 10–19 C):3.20, 1.60, 6.41, ...
© Prof. Zvi C. Koren6 19.07.10
α = 2He2+4
Ernest Rutherford
Experiment: Gold Foil, 1907
1871 – 1937, New Zealand & England
Nobel Prize in Chemistry, 1908
Conclusions:1. Most of the atom is empty space
2. Electrons (–) are in that emptiness
outside of the center (“nucleus”)
3. The nucleus is miniscule and (+).
4. The nucleus is massive.
Certain radioactive substances
emit particles:
12
3
4
+
1
2
3
4
e
e
e
ee
רדיד
© Prof. Zvi C. Koren7 19.07.10
UnitsFormula,
Value
DefinitionSymbolMeaning
lengthmaximum perpendicular displacement
from axis of propagation
AAmplitude
length/timespeed of the propagating wavevVelocity
3.00 x108 m/s(in vacuum)cSpeed of light
lengthcycle-length, length of a cycle in the waveWavelength
time–1v/number of cycles per unit timeFrequency
s–1 = cps (cycles per second)= Hz (Hertz)
length–11/cycle-number, number of cycles per length, Wavenumber
time1/time per unit cycletPeriod
Electromagnetic Radiation & Wave Properties
James Clerk Maxwell(1831 – 1879)
Scotland
© Prof. Zvi C. Koren8 19.07.10
Electromagnetic
Spectrum
E
V iolet
I ndigo
B lue
G reen
Y ellow
O range
R ed
© Prof. Zvi C. Koren9 19.07.10
Blackbody Radiation
,
“Blackbody”: Perfect absorber and emitter of radiation: Energy absorbed = Energy released
Experimental
Theoretical
If energy is absorbed
in a continuous manner:
“The Ultraviolet Catastrophe”
© Prof. Zvi C. Koren10 19.07.10
E = h
h = Planck’s constant = 6.63 x 10–34 J.s
= frequency of radiation
Basic (smallest) unit of energy that an atom can absorb (or release):
An atom can absorb or release a number of these energy units:
E = n·h, n = 1, 2, 3, …
Max Planck
Explained Blackbody Radiation Phenomenon, 1900
1858 – 1947, Germany
Nobel Prize in Physics, 1918
Conclusions:
• Energy is quantized; a “Quantum of Energy” is “h”
• An atom can absorb only specific quantities of energy
and not a continuum of energies.
Planck Equation
Planck is the “Father of Quantum Theory”
© Prof. Zvi C. Koren11 19.07.10
Albert Einstein
K.E.ejected e = Ephoton in light – Eelectron in metal
½ mv2 = h – h0
0 = threshold frequency = f(metal)
E = hPlanck: Basic (smallest) unit of energy that an atom can absorb or release
Einstein: Basic (smallest) unit of energy that a photon of light possesses
Planck-Einstein Eqn.:
e–light
metal
Explained The Photoelectric Effect Phenomenon, 1905:
Increasing intensity of light irradiation (with same frequency):
increases the number of released e’s, with same kinetic energy.
Increasing the frequency of light irradiation (with same intensity):
increases the kinetic energy of released e’s, not the number of e’s.
The Photoelectric Effect
Conclusions: Photon, Light Particle Electron (1:1)
1879 – 1955, Germany & USANobel Prize in Physics, 1921
The word “photon”
was coined in 1926 by
Gilbert N. Lewis
© Prof. Zvi C. Koren12 19.07.10
Balmer Series for Visible H Line Spectra:RH = Rydberg constant for H
= 1.097 x 107 m–1
n = 3, 4, 5, ...
Johann Jakob Balmer
Experiment: Atomic Line Spectra of Hydrogen Atoms
1825 – 1898, Switzerland
Co
nti
nu
um
Sp
ectr
um
EmissionLineSpectrum
focusingslits
prism
detector
visible partof spectrum
refraction
gas dischargetube
22H1
n
1
2
1R
prism
whitelight
Recall:
JohannesRobertRydberg
H2 2H
H H* H + light
Hi V
groundenergy
excitedenergy
Hi V
Balmer Series:
© Prof. Zvi C. Koren13 19.07.10
Atomic Line Spectra of Selected Atoms
Fantastic Web Sites:
http://www.bigs.de/en/shop/htm/termsch01.html
http://www.colorado.edu/physics/2000/quantumzone/index.html
http://jersey.uoregon.edu/vlab/elements/Elements.html
© Prof. Zvi C. Koren14 19.07.10
Generalized Balmer Equation for all Series of Lines in H-Like Atomic Ions:
22
21
H2
n
1
n
1R Z
n1 = Series I.D. = 1: Lyman Series Theodore Lyman (1874 – 1954, USA)
2: Balmer " Johann Jakob Balmer (1825–1898, Switzerland)
3: Paschen " Friedrich Paschen (1865–1947, Germany)
4: Brackett " Frederick Sumner Brackett (1896 – 1988, USA)
5: Pfund " August Herman Pfund (1879 – 1949, USA)
n2 = n1+1, n1+2, …
Other Series (or sets) of lines were also found for the H-like atoms in non-visible regions
Z = Atomic Number
© Prof. Zvi C. Koren15 19.07.10
rn = aon2/Z
1 Å = Ångstrom = 10–10 m
ao = Bohr radius = 0.529 Å
Niels Bohr
1885 – 1962, Denmark & Sweden
orbit
1 2 n=3 4
Explained the Occurrence of Atomic Line Spectra
in H-Like Atoms: Proposed a Model for the H Atom
E1 = –13.6 eV
e– in a stationary orbit
when e– jumps from one orbitto another it absorbs/releases E
e
22
21
H2
n
1
n
1R Z
En = –(13.6 eV) Z2/n2
Eif = h hc/
E = 0 eV
1 eV = 1.60 x 10–19 J
© Prof. Zvi C. Koren16 19.07.10
For a photon (particle) of light:
Ephoton
mc2 = h
c/ = = mc2/h
= h/mc = h/p
p = linear momentum = mv
Any particle of matter has a wave property:
Louis de Broglie
1892 – 1987, France
Nobel Prize in Physics, 1929
Theorized the Wave Properties of Electrons
(and Matter)
For a photon (particle) of light:
p
h
© Prof. Zvi C. Koren17 19.07.10
Wave-Particle Duality of Light & Matter
Matter
(e.g.: e-) Light
Particulate
Dalton
Thomson: e/m
Waves
Maxwell
Particulate
Einstein: “photons”
Waves
de Broglie
Schrödinger:
Applied classical wave equation
to an electron
© Prof. Zvi C. Koren18 19.07.10
Δx · Δpx > h
Heisenberg’s ??Uncertainty?? Principle
Werner Heisenberg
1901 – 1976, Germany
Nobel Prize in Physics, 1932
Uncertainty
in the position
of the e–
Uncertainty
in the momentum
of the e–
> 0·
The concept of “orbitals” is correct.
(To Be Continued)
© Prof. Zvi C. Koren19 19.07.10
Erwin Scrödinger
(1887 – 1961, Austria & Switzerland)
Schrödinger’s Wave Equation, 1926
E U
dx
d
m8
h2
2
2
2
Applied the wave equation to the electron, a particle, in the H atom (recall de Broglie)
Solution of this differential equation yields the following:
U = Potential Energy= kq1q2/r, q1=q2=e
(Coulomb’s Law)
ValueMeaningNameProperty
Function of:Spatial position;Quantum Numbers
Orbital (“electron cloud”): Describes the complex path of the electron-wave (see later)
Wave function
(same as above)Probability of finding the ewithin a small volume at acertain distance from the nucleus
Probability density2
En = –(13.6 eV) Z2/n2(K.E. + P.E.) of the e in shell nTotal energyE
rmp,n = aon2/Z
Most probable distance of the e in shell n from the nucleus
Most probable
radiusrmp
(For similar concept of average, recall the Maxwell-Boltzmann distribution.)
© Prof. Zvi C. Koren20 19.07.10
Shell, n
Subshell, ℓ
Orbital, mℓ
e–
Subshell labels are from the descriptions of the lines of atomic line:
s = sharp
p = principal
d = diffuse
f = fundamental
•••
•••
Quantum Numbers and Orbitals
Allowed ValuesStructural NameProperty NameQ.N.
1, 2, …, ShellPrincipal q.n.n
0, 1, 2, 3, 4,…, n – 1
s, p, d, f, g, …Sub-shellAngular Momentum q.n.ℓ
–ℓ , …, 0, …,+ ℓ“Orbital”Magnetic q.n.mℓ
± ½, or Electron orientationSpin q.n.ms
Questions: How many orbitals are in the 5d subshell? In the 3d? What are their q.n.’s?How many subshells are in the 4th shell? What are their q.n.’s?How many total orbitals are there in the 3rd shell? What are their q.n.’s?
Schrödinger
Pauli
© Prof. Zvi C. Koren21 19.07.10
Atomic Orbitals:Contour Plots,
Surface Boundary Plots,
90% Probability Plots
(Schrödinger)
pzpypx
s
Note the Nodes,the nodal surfaces:
Angular Planar Nodes.How many in each orbital?
Note: These orbital diagrams do not represent solid physical structures, but only probability distributions:A “Good Gambling Game”.
© Prof. Zvi C. Koren22 19.07.10
dxy dyz
2y
2x
d
Angular planar(?) surfaces.
How many in
each orbital?
General:What is the # of angular nodesin any
orbital?
2dz
dxz
© Prof. Zvi C. Koren23 19.07.10
Orbitalsmℓ valuesSubshellsℓ valuesn, Shell
1s01s01
2s02s02
2px, 2py, 2pz-1, 0, 12p1
3s03s0
3 3px, 3py, 3pz-1, 0, 13p1
-2, -1, 0, 1, 23d2
4
5
Orbitals in a Subshell in a Shell
(Complete this table)
222 zy-xyzxzxy 3d ,3d ,3d ,3d ,3d
© Prof. Zvi C. Koren24 19.07.10
1s
Dr = Radial Probability Distribution r22:
r
“Probability at a point”:Probability of finding the e in a small volume ata distance r fromthe nucleus
The probability density diagrams are “problematic” because they suggest that the greatest probability of finding the e is in the nucleus. That means that the P.E. U –r–1 –, but the total E of an e is a finite value. K.E. . Impossible!Hence these 2 plots are unrealistic.
Probability Density = 2:
The radial probability diagrams are “better”. They indicate that the probability of finding the e in the nucleus is zero. Note also, e.g., for 1s:As r increases, V of shell increases, but2 decreases. So, Dr increases then decreases.
“Probability at a distance”:Probability of finding the e in a thin spherical shell at a distance r from the nucleus.
2s3s
Dr
rrmp
rmp,1s =aon2/Z= 0.529 Å (as Bohr for fixed rn=1)
Note the radial spherical nodes.
More
Orbital
Plots
“D
ot”
Dia
gra
m
r
© Prof. Zvi C. Koren25 19.07.10
Orbital and Probability Plots
3d3p3s
2p2s
1s
Nodes:
Radial Spherical
Angular Surface
Radial Probability
Boundary Surfaceor Contour
© Prof. Zvi C. Koren26 19.07.10
Probability Densities(Probability at a point)
Summary of Different Orbital Plots
1s 2s 3s
Dr
r
Radial Probability Distribution(Probability at a Distance)
Dot Diagram
Angular Surface Nodes (planar and conical) = ℓ
Probability Density Diagram
2p23d
z
Radial Spherical Nodes = n – ℓ – 1
Total # of Nodes for a specific orbital = n – 1
Contour Plots or Boundary Surface Plots
3d
z
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