Download Chapter 7 The Electronic Structure of Atoms

The Electronic Structure
of Atoms
Chapter 7
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Properties of Waves
________________________ (l) is the distance between
identical points on successive waves.
_________________________ is the vertical distance
from the midline of a wave to the peak or trough.
________________________ (n) is the number of waves that
pass through a particular point in 1 second (Hz = 1 cycle/s).
The speed (u) of the wave = _________________
7.1
Maxwell (1873), proposed that
visible light consists of ________________________.
Electromagnetic
radiation is the
emission and
transmission of
energy in the form
of electromagnetic
waves.
Speed of light (c) in vacuum = _____________________
All electromagnetic radiation
l• n = c
7.1
A photon has a frequency of 6.0 x 104 Hz. Convert
this frequency into wavelength (nm). Does this frequency
fall in the visible region?
lxn=c
l = _______________________
l = _______________________
l = _______________________
l = _______________________
7.1
Mystery #1, “Black Body Problem”
Solved by Planck in 1900
Energy (light) is emitted or absorbed
in discrete units (quantum).
Mystery #2, “Photoelectric Effect”
Solved by Einstein in 1905
Light has both:
1. wave nature
2. particle nature
7.1
When copper is bombarded with high-energy electrons,
X rays are emitted. Calculate the energy (in joules)
associated with the photons if the wavelength of the
X rays is 0.154 nm.
E=hxn
n=c/l
E=hxc/l
E = __________________________________________
E = ______________________
7.2
Line Emission Spectrum of Hydrogen Atoms
Every element has a unique emission spectrum (p.200)
7.3
Bohr’s Model of
the Atom (1913)
1. e- can have only specific
(quantized) energy values
2. light is emitted as e- moves
from one energy level to a
lower energy level
En = -RH (
1
n2
)
n (principal quantum number) = 1,2,3,…
RH (Rydberg constant) = 2.18 x 10-18J
7.3
Bohr showed the energy a H
atom can have is equal to:
En = -RH (
1
n2
)
Ephoton = DE = Ef - Ei
1
Ef = -RH ( 2
nf
1
Ei = -RH ( 2
ni
1
DE = RH( 2
ni
)
)
1
n2f
)
RH is the Rydberg constant
pp.200-202
n is the principal quantum number
7.3
Calculate the wavelength (in nm) of a photon
emitted by a hydrogen atom when its electron
drops from the n = 5 state to the n = 3 state.
Ephoton = DE = RH(
1
n2i
1
n2f
)
Ephoton = 2.18 x 10-18 J x (1/25 - 1/9)
Ephoton = DE = -1.55 x 10-19 J
Ephoton = h x c / l
l = h x c / Ephoton
l = ________________________
7.3
Why is e- energy quantized?
De Broglie (1924) reasoned that
e- is both particle and wave.
2pr = nl
l = h/mu
u = velocity of em = mass of ep.204
7.4
What is the de Broglie wavelength (in nm)
associated with a 2.5 g Ping-Pong ball
traveling at 15.6 m/s?
l = h/mu
h in J•s m in kg u in (m/s)
l = ____________________________________
l = ____________________________________
7.4
Schrödinger Wave Equation
In 1926 _________________ wrote an equation that
described both the particle and wave nature of the e____________________ (Y, psi) describes:
1. energy of e- with a given Y
2. probability of finding e- in a volume of space
Schrödinger’s equation can be solved exactly only
for ___________________________________.
We must approximate its solution for multi-electron
systems.
7.5
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
______________________________ n
n = 1, 2, 3, 4, ….
n=3
n=2
n=1
distance of e- from the nucleus
7.6
Where 90% of the
e- density is found
for the 1s orbital
e- density (1s orbital) falls off rapidly
as distance from nucleus increases
7.6
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
______________________________ l
for a given value of n, l = 0, 1, 2, 3, … n-1
n = 1, l = 0
n = 2, l = 0 or 1
n = 3, l = 0, 1, or 2
l=0
l=1
l=2
l=3
s orbital
p orbital
d orbital
f orbital
Shape of the “volume” of space that the e- occupies
7.6
l = 0 (s orbitals)
l = 1 (p orbitals)
7.6
l = 2 (d orbitals)
7.6
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
______________________________ ml
for a given value of l
ml = -l, …., 0, …. +l
if l = 1 (p orbital), ml = -1, 0, or 1
if l = 2 (d orbital), ml = -2, -1, 0, 1, or 2
orientation of the orbital in space
7.6
ml = -1
ml = -2
ml = 0
ml = -1
ml = 0
ml = 1
ml = 1
ml = 2
7.6
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
______________________ ms
ms = ______ or ______
ms = +½
ms = -½
7.6
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
Existence (and energy) of an electron in an atom is
described by its ______________ wave function Y.
________________________ — no two electrons in
an atom can have the same four quantum numbers.
Each seat in a stadium is uniquely identified (E, R12, S8)
Each seat can hold only one individual at a time
7.6
Magnetic properties of atoms
Paramagnetic atoms are attracted to a magnet.
Any atom with an odd number of electrons is paramagnetic.
Diamagnetic atoms are slightly repelled by a magnet.
Atoms with an even number of electrons may be either
paramagnetic or diamagnetic:
•If there are unpaired electrons, it is paramagnetic
•If there are no unpaired electrons, it is diamagnetic
p.215
_____________________
unpaired electrons
2p
______________________
all electrons paired
2p
7.8
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
_______________ – electrons with the same value of n
_________– electrons with the same values of n and l
_______– electrons with the same values of n, l, and ml
7.6
Schrödinger Wave Equation
Y = fn(n, l, ml, ms)
How many electrons can an orbital hold?
If n, l, and ml are fixed, then ms = ½ or - ½
Y = (n, l, ml, ½) or Y = (n, l, ml, -½)
An orbital can hold _______ electrons
7.6
How many 2p orbitals are there in an atom?
n=2
If l = 1, then ml = -1, 0, or +1
2p
l=1
___ orbitals
7.6
How many electrons can be placed in the
3d subshell?
n=3
3d
If l = 2, then ml = -2, -1, 0, +1, or +2
l=2
_____ orbitals which can hold a total of _____ e-
7.6
Energy of orbitals in a ____________ electron atom
Energy depends only on principal quantum number n
n=3
n=2
En = -RH (
1
n2
)
n=1
7.7
Energy of orbitals in a ___________-electron atom
Energy depends on n and l
n=3 l = 2
n=3 l = 0
n=2 l = 0
n=3 l = 1
n=2 l = 1
n=1 l = 0
7.7
Fill lowest energy orbitals first (______________ principle)
H 1 electron
H 1s1
7.7
Fill lowest energy orbitals first (Aufbau principle)
He 2 electrons
He 1s2
7.7
Fill lowest energy orbitals first (Aufbau principle)
Li 3 electrons
Li 1s22s1
7.7
Fill lowest energy orbitals first (Aufbau principle)
Be 4 electrons
Be 1s22s2
7.7
Fill lowest energy orbitals first (Aufbau principle)
B 5 electrons
B 1s22s22p1
7.7
Fill lowest energy orbitals first (Aufbau principle)
?
C 6 electrons
C 1s22s22p2
7.7
______________: The most stable arrangement of electrons in subshells is the one
with the greatest number of parallel spins.
C 6 electrons
C 1s22s22p2
7.7
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
?
N 7 electrons
N 1s22s22p3
7.7
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
N 7 electrons
N 1s22s22p3
7.7
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
O 8 electrons
O 1s22s22p4
7.7
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
F 9 electrons
F 1s22s22p5
7.7
Hund’s rule: The most stable arrangement
of electrons in subshells is the one with the
greatest number of parallel spins.
Ne 10 electrons
Ne 1s22s22p6
7.7
Order of orbitals (filling) in multi-electron atom
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
7.7
What is the electron configuration of Mg?
Mg 12 electrons
1s < 2s < 2p < 3s < 3p < 4s
___________________ 2 + 2 + 6 + 2 = 12 electrons
Abbreviated as [Ne]______
[Ne] is 1s22s22p6
7.7
What are the possible quantum numbers for the
last (outermost) electron in Cl?
Cl 17 electrons
1s < 2s < 2p < 3s < 3p < 4s
____________________ 2 + 2 + 6 + 2 + 5 = 17 electrons
Last electron added to 3p orbital
n=3
l=1
ml = -1, 0, or +1
ms = ½ or -½
7.7
Outermost subshell being filled with electrons
7.8
______________________
unpaired electrons
2p
______________________
all electrons paired
2p
7.8