Transcript Ch7lsn21Chem105

CHAPTER 7
Atomic Structure
Road Map
Test 2 Extra credit Collection
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Chem 105 Chpt 7 Lsn 21
Equations
speed of light = wavelength x frequency
c = λ X  = 3.00 x 108 m/s
 E = nh = nh(c/) n= positive integer

Planck’s constant(h) = 6.626 x 10–34 J s
 Eatom = Eemitted (or absorbed) radiation = nh

Rydberg equation

=R
n2 > n1
R = 1.096776 x 107 m-1
 ΔE = Efinal – Einitial = –2.18 x 10–18 J
 Ephoton = Estate A – Estate B = hν

Chem 105 Chpt 7 Lsn 21
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Old Dead Dudes
Planck – blackbody radiation; hot glowing
object; emit or absorb certain discrete quanta
of energy
 Bohr – one electron model; spectral lines
explained; e- motion restricted to fixed orbits
 Einstein – explained photoelectric effect - flow
of current when monochromatic light of
sufficient energy hits an object
 Rydberg – predicted energy levels

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Chem 105 Chpt 7 Lsn 21
Practice Problem 21-1
 The
frequency of electromagnetic
radiation of wavelength 5.6 mm is
A) 5.4 x 107 Hz
B) 1.9 x 10-11 Hz
C) 5.4 x 1010 Hz
D) 1.1 x 108 Hz
E) none of the above
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21-1 Answer
 The
frequency of electromagnetic
radiation of wavelength 5.6 mm is
A) 5.4 x 107 Hz
B) 1.9 x 10-11 Hz
C) 5.4 x 1010 Hz
D) 1.1 x 108 Hz
E) none of the above
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21-2 (7.12) Answer

7.12 540 nm (10-9m/1nm)= 5.4  10–7 m
E=
=
=
= 3.7  10–19 J/photon
This radiation does not have enough energy(6.7
x 10-19 J/atom) to activate the switch. This is also
true for radiation with wavelengths greater than 540
nm.
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Chem 105 Chpt 7 Lsn 21
Bohr Model
Energy of atoms quantized;
photon emitted when edecreases in orbit
- Spectral line from emission
Emission - higher to lower energy
state
Absorption – lower to higher
energy state
n = quantum number
- Lower n: smaller radius
of orbit (space e- circling in)
- Ground state: n=1
- Excited state: n>1
Chem 105 Chpt 7 Lsn 21
Quantum staircase
7
7.20 Which of these electron transitions
correspond to absorption of energy
and which to emission?
Absorption
(a) n = 2 to n = 4
Emission
(b) n = 3 to n = 1
Emission
(c) n = 5 to n = 2
Absorbtion
(d) n = 3 to n = 4
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Chem 105 Chpt 7 Lsn 21
The Bohr explanation of the three
series of spectral lines.
n=2 visible
n=3 infrared
n=1 ultraviolet
Numerous atoms with
different excitation states (n)
and subsequent  of emission
Chem 105 Chpt 7 Lsn 21
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Practice Problem 21.3
 How
much energy is absorbed when
an electron is excited from the first
level to the fourth?
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21.3 Answer
 How
much energy is absorbed when
an electron is excited from the first
level to the fourth?
2.04 x 10-18 J
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21.4
 Calculate
the frequency of the light
emitted by a hydrogen atom during a
transition of its electron from the n = 3
to n = 1 energy level, based on the
Bohr theory.
A) 2.92 x 1015 s-1
B) 1.94 x 10-18 s-1
C) 3.21 x 1015 s-1
D) 3.05 x 10-15 s-1
E) Not enough information given to
calculate answer.
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21.4 Answer
 Calculate
the frequency of the light
emitted by a hydrogen atom during a
transition of its electron from the n = 3
to n = 1 energy level, based on the
Bohr theory.
A) 2.92 x 1015 s-1
B) 1.94 x 10-18 s-1
C) 3.21 x 1015 s-1
D) 3.05 x 10-15 s-1
E) Not enough information given to
calculate answer.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of
the Atom
 Acceptance
of the dual nature of
matter and energy and of the
uncertainty principle culminated in the
field of quantum mechanics, which
examines the wave motion of objects
on the atomic scale. In 1926, Erwin
Schrödinger derived an equation that is
the basis for the quantum-mechanical
model of the hydrogen atom.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom: The Atomic
Orbital and the Probable Location of the Electron

Each solution to the equation is associated
with a given wave function, also called an
atomic orbital. It’s important to keep in
mind that an “orbital” in the quantummechanical model bears no resemblance to
an “orbit” in the Bohr model: an orbit was
an electron’s path around the nucleus,
whereas an orbital is a mathematical
function with no direct physical meaning.
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Chem 105 Chpt 7 Lsn 21
Quantum Numbers and Atomic
Orbitals
 An atomic orbital is specified by
.
three quantum numbers.
n the principal quantum number; distance
from nucleus (size); n = 1,2,3…
l the angular momentum quantum
number; shape; l = 0 to n-1
ml the magnetic moment quantum
number; orbital orientation; – ml =-l to +l
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Chem 105 Chpt 7 Lsn 21
n = LEVELS
Smaller n, the lower the energy level the
greater the probability of the electron being
closer to the nucleus
 l = orbital shape

l
=0
l=1
l=2
l=3
s
p
d
f
spherical
dumb bell & crash and burn, Fig 7.18
cloverleaf, Fig 7.19
too complicated
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom: Quantum
Numbers of an Atomic Orbital



Sublevel (subshell) : designate the orbital
shape. Each sublevel has a letter designation:
 ℓ = 0 is an s sublevel
 ℓ = 1 is a p sublevel.
Smart People
 ℓ = 2 is a d sublevel.
Don’t Fail
 ℓ = 3 is an f sublevel.
Orbital. Each allowed combination of n, ℓ, and
mℓ values specifies one of the atom’s orbitals.
Thus, the three quantum numbers that
describe an orbital express its size (energy),
shape, and spatial orientation .
The total number of orbitals for a given n value
is n2.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom:
Shapes of Atomic Orbitals
 Orbitals
with Higher ℓ Values
with ℓ = 3 are f orbitals and must
have a principle quantum number of at
least n = 4. There are seven f orbitals (2ℓ
+ 1 = 7), each with a complex, multilobed shape.
 Orbitals
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom: Energy
Levels of the Hydrogen Atom
 The
energy state of the H atoms
depends on the principal quantum
number n only.
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Chem 105 Chpt 7 Lsn 21
CLASSICAL THEORY
Matter
particulate,
massive
Energy
continuous,
wavelike
Summary of the major observations
and theories leading from classical
theory to quantum theory.
Since matter is discontinuous and particulate
perhaps energy is discontinuous and particulate.
Observation
blackbody radiation
Theory
Planck:
photoelectric effect
Energy is quantized; only certain values
allowed
Einstein: Light has particulate behavior (photons)
atomic line spectra
Bohr:
Energy of atoms is quantized; photon
emitted when electron changes orbit.
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21.5
Determining
Quantum Numbers for an Energy Level
PROBLEM:
What values of the angular momentum (l) and
magnetic (ml) quantum numbers are allowed for a
principal quantum number (n) of 3? How many
orbitals are allowed for n = 3?
PLAN: Follow the rules for allowable quantum numbers found in the text.
l values can be integers from 0 to n-1; ml can be integers from -l
through 0 to + l.
SOLUTION: For n = 3, l = 0, 1, 2
For l = 0 ml = 0
For l = 1 ml = -1, 0, or +1
For l = 2 ml = -2, -1, 0, +1, or +2
There are 9 ml values and therefore 9 orbitals with n = 3.
Chem 105 Chpt 7 Lsn 21
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Practice Problem 21.6
Determining
Sublevel Names and Orbital Quantum
Numbers
PROBLEM: Give the name, magnetic quantum numbers, and
number of orbitals for each sublevel with the following
quantum numbers:
(a) n = 3, l = 2
(b) n = 2, l = 0
(c) n = 5, l = 1
(d) n = 4, l = 3
PLAN: Combine the n value and l designation to name the sublevel.
Knowing l, we can find ml and the number of orbitals.
SOLUTION:
n
l
sublevel name possible ml values # of orbitals
(a)
3
2
3d
-2, -1, 0, 1, 2
5
(b)
2
0
2s
0
1
(c)
5
1
5p
-1, 0, 1
3
(d)
4
3
4f
-3, -2, -1, 0, 1, 2, 3
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Chem 105 Chpt 7 Lsn 21
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Practice Problem 21.7 What is wrong with
this picture, or complete the name.
n
1
l
1
ml
0
name
1p
4
3
1
4d
3
2
-2
?
?
?
?
2s
2
1
0
?
3
1
-2
3p
Chem 105 Chpt 7 Lsn 21
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The Quantum-Mechanical Model of the Atom: Quantum
Numbers of an Atomic Orbital
 The
energy states and orbitals of the
atom are described with specific terms
and associated with one or more
quantum numbers.
1. Level
(n). The atom’s energy levels, or
shells, are given by the n value: the
smaller the n value, the lower the energy
level and the greater the probability of
the electron being closer to the nucleus.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom: Quantum
Numbers of an Atomic Orbital
2.
Sublevel (ℓ). The atom’s levels contain
sublevels, or subshells, which
designate the orbital shape. Each
sublevel has a letter designation:
a. ℓ = 0 is an s sublevel
b. ℓ = 1 is a p sublevel.
c. ℓ = 2 is a d sublevel.
d. ℓ = 3 is an f sublevel.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom: Quantum
Numbers of an Atomic Orbital
3.
Orbital (mℓ ). Each allowed combination
of n, ℓ, and mℓ values specifies one of
the atom’s orbitals. Thus, the three
quantum numbers that describe an
orbital express its size (energy), shape,
and spatial orientation .
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21-8
value or values of mℓ are
allowable for an orbital with ℓ = 2?
A) 0
B) 2
C) -1
D) none of the above
E) all of the above
 What
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21-8 Answer
value or values of mℓ are
allowable for an orbital with ℓ = 2?
A) 0
B) 2
C) -1
D) none of the above
E) all of the above
 What
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom:
Shapes of Atomic Orbitals
 The
s Orbital
 An
orbital with ℓ = 0 has a spherical
shape with the nucleus at its center and
is called an s orbital.
 The 2s orbital (Figure 7.17B) has two
regions of higher electron density.
Between the two regions is a spherical
node, a shell-like region where the
probability drops to zero.
Chem 105 Chpt 7 Lsn 21
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Practice Problem 21-9
nodes for a 3s atomic orbital are
A) two points near the nucleus and
another point at an infinite distance
from the nucleus.
B) three spherical solids.
C) one plane and two spheres.
D) two concentric circles.
E) two concentric spheres.
 The
Chem 105 Chpt 7 Lsn 21
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Practice Problem 21-9 Answer
nodes for a 3s atomic orbital are
A) two points near the nucleus and
another point at an infinite distance
from the nucleus.
B) three spherical solids.
C) one plane and two spheres.
D) two concentric circles.
E) two concentric spheres.
 The
Chem 105 Chpt 7 Lsn 21
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The Quantum-Mechanical Model of the Atom:
Shapes of Atomic Orbitals

The p Orbital
 An
orbital with ℓ = 1 has two regions (lobes) of
high probability, one on either side of the
nucleus, and is called a p orbital. In Figure
7.18, the nucleus lies at the nodal plane of this
dumbbell-shaped orbital. Keep in mind that
one p orbital consists of both lobes and that the
electron spends equal time in both.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom:
Shapes of Atomic Orbitals

The p Orbital
there are three mℓ values, these describe
the three mutually perpendicular orientations in
space. Unlike an s orbital, each p orbital does
have a specific orientation in space. The ℓ = 1
value has three possible mℓ values: –1, 0, and
+1, which refer to three mutually perpendicular
p orbitals. They are identical in size, shape,
and energy, differing only in orientation.
 Since
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom:
Shapes of Atomic Orbitals
 The d Orbital
 An orbital with ℓ = 2 is called a d orbital.
There are five possible mℓ values for the
ℓ = 2 value: –2, –1, 0, +1, +2.
 Thus, a d orbital can have any one of five
orientations, as shown in Figure 7.19.
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Chem 105 Chpt 7 Lsn 21
The Quantum-Mechanical Model of the Atom:
Shapes of Atomic Orbitals
 Orbitals
with Higher ℓ Values
with ℓ = 3 are f orbitals and must
have a principle quantum number of at
least n = 4. There are seven f orbitals (2ℓ
+ 1 = 7), each with a complex,
multilobed shape; Figure 7.20 shows one
of them.
 Orbitals
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Chem 105 Chpt 7 Lsn 21
Practice Problem 21-10
 According
to the quantum-mechanical
model, how many orbitals in a given
atom have n = 3?
A) 4
B) 7
C) 9
D) 10
E) 18
Chem 105 Chpt 7 Lsn 21
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Practice Problem 21-10 Answer
 According
to the quantum-mechanical
model, how many orbitals in a given
atom have n = 3?
A) 4
B) 7
C) 9
D) 10
E) 18
Chem 105 Chpt 7 Lsn 21
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Next Lesson

Chapter 8
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Chem 105 Chpt 7 Lsn 21