chapter 6: electronic structure of atoms light is a form of electromagnetic radiation (emr): an...
TRANSCRIPT
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Light is a form of electromagnetic radiation (EMR):
• an oscillating charge, such as an electron, gives rise to electromagnetic radiation:
Electric Field
Magnetic Field
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
• Both the Electric and the Magnetic field propagate through space
• In vacuum, both move at the speed of light (3 x 108 m/s)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Electromagnetic radiation is characterized by
• wavelength (), or frequency ()
and
• amplitude (A)
A = intensity
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Frequency measures how many wavelengths pass a point per second:
1 s
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Electromagnetic radiation travels at the speed of light:
c = 3 x 108 m s-1
Relation between wavelength, frequency, and amplitude:
c =
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
400 nm 750 nm
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Red Orange Yellow Green Blue Ultraviolet
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the wavelength, in m, of radiowaves transmitted bythe local radio station WHQR 91.3 MHz?
c
c m29.3
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
A certain type of laser emits green light of 532 nm. What frequency does this wavelength correspond to?
c
c 1141064.5 s
Hz141064.5
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Classically, electromagnetic radiation (EMR) was thought to have only wave-like properties.
Two experimental observations challenged this view:
Blackbody radiation
Photoelectric Effect
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Blackbody radiation
• Hot objects emit light
• The higher T, the higherthe emitted frequency
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Blackbody radiation
Brightness
wavelength ()
visible region
T2
T1
prediction of classical theory
= there would be NO DARKNESS
“ultraviolet catastrophe”
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Blackbody radiation
• light is emitted by oscillators
• high energy oscillators require a minimum amount of energy to be excited:
E = h
• energy is not provided by temperature in “black body”
Max Planck (1858 - 1947)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Blackbody radiation
E = h
Planck’s constant = 6.63 x 10-34 J s
frequency of oscillator
Energy of radiation is related to frequency, not intensity
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the energy of a photon of electromagnetic radiation that has a frequency of 400 kHz?
hE
= 2.65 x 10-28 J
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Photoelectric Effect
Albert Einstein (1879-1955)
e- e- e-
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Photoelectric Effect
Albert Einstein (1879-1955)
e- e- e-
e-
• Light of a certain minimum frequency is required to dislodge electrons from metals
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Photoelectric Effect
• Ability of light to dislodge electrons from metals is related to its frequency, not intensity
E = h
• This means that light comes in “units” of h
• The h “unit” is called a quantum of energy
• A quantum of light (EMR) energy = photon
• Intensity is related only to the number of “units”
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Relationship between Energy, Wavelength, and Frequency:
c hE
c
hE
hEc
ch
E
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the energy of a photon of light of 532 nm?
ch
E
= 3.74 x 10-19 J
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
or
E = h
Electromagnetic Radiation
wavestream of particles
(photons)
Whether light behaves as a wave or as a stream of photons depends on the method used to investigate it !
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Understanding light in terms of photons helped understand atomic structure
many light sources produce a continuous spectrum
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Thermally excited atoms in the gas phase emit line spectra
continuous spectrum (all wavelengths together: white light)
line spectrum (only some wavelengths: emission will have a color)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Photograph of the H2 line spectrum (Balmer series) in the visible region
(1825-1898)
Johann Balmer (1825-1898)
2
2
2
1
111nn
RH
Rydberg constant1.097 x 107 m-1 positive integers
(e.g. 1,2,3, etc)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Niels Bohr was the first to offer an explanation for line spectra
Bohr Model of the Hydrogen Atom
• Only orbits of defined energy and radii are permitted in the hydrogen atom
• An electron in a permitted orbit has a specific energy and will not radiate energy and will not spiral into the nucleus
• Energy is absorbed or emitted by the electron as the electron moves from one allowed orbit into another. Energy is absorbed or emitted as a photon of E = h
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Niels Bohr was the first to offer an explanation for line spectra
(1885-1962)
electron orbits
Bohr’s Model of the Hydrogen Atom
n = 1n = 2n = 3n = 4n = 5n = 6
nucleus
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Bohr’s Model of the Hydrogen Atom
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
nucleus
eabsorption of a photon
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Bohr’s Model of the Hydrogen Atom
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
nucleus
e
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Bohr’s Model of the Hydrogen Atom
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
nucleus
e “excited state”
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Bohr’s Model of the Hydrogen Atom
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
nucleus
e
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Bohr’s Model of the Hydrogen Atom
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
nucleus
e emission of a photon
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n = 6n = 5n = 4
n = 3
n = 2
n = 1
Energy
Ground State
nucleus
(a) (b) (c)
Which of these transitions representsan absorption process?
Which of these transitions involves thelargest change in energy?
Which of these transitions leads to theemission of the longest wavelength photon?
Does this wavelength correspond to a high or low frequency?
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Transitions corresponding tothe Balmer series
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n = 6n = 5n = 4
n = 3
n = 2
n = 1
n = Principal Quantum Number (main energy levels)
4
11018.2 18 JE
JE 181018.2
9
11018.2 18 JE
Energy of electron in a given orbit:
2
1n
RchE H
h=Planck’s constant, c=speed of light, RH = Rydberg constant
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n = 6n = 5n = 4
n = 3
n = 2
n = 1
2
1
final
Hfinal nRchE
For an electron moving from n = 4 to n = 2:
2
1
initial
Hinitial nRchE
initialfinal EEE
22
11
initial
H
final
H nRch
nRchE
22
11
initialfinal
H nnRchE
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n = 6n = 5n = 4
n = 3
n = 2
n = 1
For an electron moving from n = 4 to n = 2:
22
11
initialfinal
H nnRchE
22 4
1
2
1HRchE
16
1
4
11018.2 18 JE
1875.01018.2 18 JE
E = - 4.09 x 10-19 J
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n = 6n = 5n = 4
n = 3
n = 2
n = 1
E = 4.09 x 10-19 J
What wavelength (in nm) does this energy correspond to?
ch
E Ech
JmsJs
19
1834
1009.41031063.6
The energy of the photon emitted is:
= 486 x 10-9 m
= 486 nm
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n=6 → n=2
n=5 → n=2
n=4 → n=2 n=3 → n=2
Balmer Series
= 486 nm
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
The Wave Behavior of Matter
If light can behave like a stream of particles (photons)…
… then (small) particles should be able to behave like waves, too
vmh
For a particle of mass m, moving at a velocity v:
De Broglie Wavelength
e.g electrons have a wavelength (electron microscope!)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
The Uncertainty Principle
Werner Heisenberg (1901-1976)and Niels Bohr
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
The Uncertainty Principle
It is impossible to know both the exact position and the exact momentum of a subatomic particle
4h
mx v
uncertainty in position, x
uncertainty in momentum, mv
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Erwin Schrödinger (1887-1961)
Quantum Mechanics and Atomic Orbitals
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Quantum Mechanics and Atomic Orbitals
• Schrödinger proposed wave mechanical model of the atom
• Electrons are described by a wave function, ψ
• The square of the wave function, ψ2, provides information onthe location of an electron (probability density or electron density)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Quantum Mechanics and Atomic Orbitals
• the denser the stippling, thehigher the probability of findingthe electron
• shape of electron densityregions depends on energy ofelectron
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
or
n = 1
n = 1
orbit
orbitalz
x
y
Bohr’s model:
Schrödinger’s model:
electron circles around nucleus
electron is somewherewithin that spherical region
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Bohr’s model:
Schrödinger’s model:
• requires only a single quantum number (n) to describe an orbit
• requires three quantum numbers (n, l, and m) to describe an orbital
n: principal quantum numberl : second or azimuthal quantum numberml: magnetic quantum number
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
(1) n = principal quantum number (analogous to Bohr model)
- the higher n, the higher the energy of the electron
- energy of electron in a given orbital:
2
1n
RchE H
Schrödinger’s model:
- is always a positive integer: 1, 2, 3, 4 ….
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
(2) l = azimuthal quantum number
Schrödinger’s model:
- takes integral values from 0 to n-1 n = 3e.g.
- l is normally listed as a letter:
Value of l: 0 1 2 3letter: s p d f
- l defines the shape of an electron orbital
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Schrödinger’s model:
z
x
y
s-orbital p-orbital(1 of 3)
d-orbital(1 of 5)
f-orbital(1 of 7)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
(3) ml = magnetic quantum number
Schrödinger’s model:
- takes integral values from -l to +l, including 0
l = 2e.g.
- ml describes the orientation of an electron orbital in space
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Shells:
• are sets of orbitals with the same quantum number, n
Subshells:
• are orbitals of one type within the same shell
• a shell of quantum number n has n subshells
• total number of orbitals in a shell is n2
4f subshell
n=3 shell
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
n = 1 2 43
l = 0 0, 1 0, 1, 2 0, 1, 2, 3
1s 2s, 2p 3s, 3p, 3d 4s, 4p, 4d, 4f
ml = 0 0, -1,0,1 0; -1,0,1; -2,-1,0,1,2 0; -1,0,1; -2,-1,0,1,2; -3,-2,-1,0,1,2,3
# orbitalsin subshell
1 1 3 1 3 5 1 3 5 7
Total # of orbitalsin shell
1 4 9 16
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
1st floor
2nd floor
3rd floor
standard-room
2s-room
3s-room
2promotion-room
3p-room 3deluxe-room
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Orbital energy levelsin the Hydrogen Atom
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the designation for the n=3, l=2 subshell ?
What are the possible values for ml for each of these orbitals ?
How many orbitals are in this subshell ?
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Which of the following combinations of quantum numbersis possible?
n=1, l=1, ml= -1
n=3, l=2, ml= 1
n=2, l=1, ml= -2
n=3, l=0, ml= -1
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Representation of Orbitals
1s 2s 3s
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Representation of Orbitals
2p orbitals
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Representation of Orbitals
all three p orbitals
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Representation of Orbitals
3d orbitals
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Which combination of quantum numbers is possible for theorbital shown below?
(a) n=1, l=0, ml= 0
(b) n=2, l=-1, ml= 1
(c) n=3, l=3, ml= -2
(d) n=3, l=2, ml= -1
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
There is a fourth quantum number that characterizes electrons:
spin magnetic quantum number, ms
ms can only take two values, +1/2 or -1/2
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Wolfgang Pauli (1900-1958) A. Einstein & W. Pauli
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Pauli’s Exclusion Principle:
No two electrons in an atom can have the same set of 4 quantum numbers, n, l, ml, and ms
For a given orbital, e.g. 2s, n, l, ml are fixed:
n=2, l=0, ml =0
=> an orbital can only contain two electron if they differ in ms
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
2s 2p
A maximum of 2 electron can occupy one orbital, IF these two electrons have opposite spin:
n=2, l=0, ml =0, ms = +1/2n=2, l=0, ml =0, ms = -1/2
arrows pointing up/down indicate electron spin
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Energy levels in the hydrogen atom:
all subshells of a given shellhave the same energy
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Energy levels in many-electron atoms:
• In many-electron atoms, the energy of an orbital increases with l, for a given n
• In many-electron atoms, the lower energy orbitals get filled first
• orbitals with the same energy are said to be
degenerate
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Electron Configurations:
1H 1s1
2He
3Li
4Be
6C
7N
10Ne
11Na
1s2
1s22s1
1s22s2
1s22s22p2
1s22s22p3
1s22s22p6
1s22s22p63s1
Line Notation:
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
7N 1s22s22p3
Hund’s Rule:
For degenerate orbitals, the energy is minimized when the number of electrons with the same spin is maximized
Electron Configurations:
=> degenerate orbitals (p, d, etc)get filled with one electron each first (same spin).
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
the Aufbau Principle helps you to remember the order in which orbitals get filled:
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d 6f
7s 7p 7d 7f
[Ne]
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
14Si 1s22s22p63s23p2 Line notation
orbital diagram(no energy info)
s
p
d
1
2
3
Condensed line notation
“core electrons”
3s23p2
“valence (outer shell) electrons”
1s22s22p63s23p2
[Ne]
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
14Si Line notation
orbital diagram(no energy info)
s
p
d
1
2
3
Condensed line notation3s23p2
Valence electrons take part in bonding
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of Cl?
s
p
d
1
2
3
valence electrons (7)
17Cl :
core electrons =
electron configurationof the preceding noble gas
3s23p5[Ne]
valence electrons (2)
core electrons =
electron configurationof the preceding noble gas
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of Ca?
s
p
d
1
2
3
20Cl : 4s2
4
f
(4s orbital is filled before 3d !)[Ar]
valence electrons (7)
core electrons =
electron configurationof the preceding noble gas
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of Br?
s
p
d
1
2
3
35Br : 3d104s24p5
4
f
(4s orbital is filled before 3d !)[Ar]
For main group elements,electrons in a filled d-shell(or f-shell) are not valenceelectrons
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
Does it matter in which order the electron configuration is written ?
s
p
d
1
2
3
35Br : 1s22s22p63s23p63d104s24p5
4
f
1s22s22p63s23p64s23d104p5or:
ordered by orbital number
ordered by energy
NO, both are correct!
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
s
p
d
1
2
3
4
f
What is the electron configuration of vanadium (V)?
23V: [Ar] 3d34s2
core electrons =
electron configurationof the preceding noble gas
valence electrons (5)
(4s orbital is filled before 3d !)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
s
p
d
1
2
3
4
f
What is the electron configuration of chromium (Cr)?
24Cr: [Ar] 3d54s1
[Ar] 3d44s2 is less stable than [Ar] 3d54s1
A half-filled or completely filled d-shell is a preferred configuration
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
1s
2s 2p
3s 3p
4s
3d
4p
4f
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of the Ca ion?
s
p
d
1
2
3
20Ca : 4s2
4
f
[Ar]
20Ca2+ : [Ar]
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
● Atoms tend to gain or lose the number of electrons
needed to achieve the
electron configuration of the closest noble gas
● Metals tend to lose electrons to form cations
● Nonmetals tend to gain electrons to form anions
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of the ion formed by Se?
s
p
d
1
2
3
34Se : 3d104s24p4
4
f
[Ar]
34Se2- : [Ar] 3d104s24p6 = [Kr]
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of the ion formed by Br?
s
p
d
1
2
3
35Br : 3d104s24p5
4
f
[Ar]
35Br- : [Ar] 3d104s24p6 = [Kr]
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electronic structure of the ion formed by Rb?
s
p
d
1
2
3
37Rb : 5s1
4
f
[Kr]
37Rb+ : [Kr]
5
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
37Rb+ :
35Br- : [Ar] 3d104s24p6 = [Kr]
34Se2- : [Ar] 3d104s24p6 = [Kr]
[Ar] 3d104s24p6 = [Kr]
37Rb+35Br-
34Se2- , , , and 36Kr have the same electron configuration:
they are isoelectronic
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
a.
b.
c.
d.
Which of the four orbital diagrams written below for nitrogen violates the Pauli Exclusion Principle?
violates Hund’s rule(all spins must point in the same direction)
violates Hund’s rule(degenerate orbitals get one electron each, first)
doesn’t violate anything
violates Pauli’s Exclusion Principlethere are two same spin electrons in one orbital, i.e. all 4 quantum numbers are the
same – which is impossible1s 2s 2p
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the total number of orbitals in the fourth shell (n=4) ?
a. 16 b. 12 c. 4 d. 3
n=4
l = 0 1 2 3s p d f
ml = 0 -1,0,1 -2,-1,0,1,2 -3,-2,-1,0,1,2,3
one s + three p + five d + 7 f orbitals
=16 orbitals
what is the total number of different s,p, d and f orbitals?
(n2)
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the number of subshells in the third shell (n=3) ?
a. 18 b. 9 c. 3 d. 1
n=3
l = 0 1 2s p d
How many different types of orbitals are there?
Chapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of Atoms
What is the electron configuration of the sodium cation, Na+ ?
a. 1s22s22p63s1 b. 1s22s22p6
c. 1s22s22p63s2 d. 1s22s22p7
11Na+ = 11 electrons -1 = 10 electrons
1s2 2s2 2p6