Quantum Calculations
Electronic
Structure
of Atoms
• Objectives
• Explain the theories behind how electrons move
as particles and waves
Apply the relationship between
wavelength, frequency, mass and energy
to solving calculations
• Informal assessment – monitoring
student questions and discussions as
we complete the notes and the practice
problems
• Formal assessment – analyzing student
responses to the warm up, exit ticket Electronic
Structure
of Atoms
and practice problems
Lesson Sequence
• Evaluate: Warm Up
• Explain: Quantum Calculations Notes
• Elaborate: Quantum Calculations
Practice
• Evaluate: Closure
Electronic
Structure
of Atoms
Warm Up
• What is the energy of the red light that
has a wavelength of 675 nm?
Electronic
Structure
of Atoms
Objectives
• Today I will be able to:
 Explain the theories behind how electrons
move as particles and waves
Apply the relationship between
wavelength, frequency, mass and energy
to solving calculations
Electronic
Structure
of Atoms
Homework
• Quantum Calculations Homework
• Chapter 6 Book Problems (15th edition)
 The wave nature of light – 6.19, 6.21, 6.25, 6.27, 6.31
 Bohr Model – 6.37, 6.39, 6.45, 6.47
 Quantum Mechanics and Atomic Orbitals – 6.55, 6.57,6.59,
6.61, 6.75,
 Electron Configuration - 6.77, 6.79
 Additional Exercises – 6.93, 6.102
Electronic
Structure
of Atoms
Quantum Calculations
Electronic
Structure
of Atoms
What is the relationship
between wavelength and
frequency?
Electronic
Structure
of Atoms
Waves
• To understand the electronic structure of
atoms, one must understand the nature of
electromagnetic radiation.
• The distance between corresponding points
Electronic
on adjacent waves is the wavelength ().
Structure
of Atoms
Waves
• The number of waves
passing a given point per
unit of time is the
frequency ().
• For waves traveling at
the same velocity, the
longer the wavelength,
the smaller the
frequency.
Electronic
Structure
of Atoms
Electromagnetic Radiation
• All electromagnetic
radiation travels at the
same velocity: the
speed of light
• (c) = 3.00  108 m/s.
• Therefore,
c = 
Electronic
Structure
of Atoms
The Nature of Energy
• The wave nature of light
does not explain how
an object can glow
when its temperature
increases.
• Max Planck explained it
by assuming that
energy comes in
packets called quanta.
Electronic
Structure
of Atoms
The Nature of Energy
• Einstein used this
assumption to explain the
photoelectric effect.
• He concluded that energy
is proportional to
frequency:
E = h
where h is Planck’s
constant, 6.63  10−34 J-s.
Electronic
Structure
of Atoms
The Nature of Energy
• Therefore, if one knows the
wavelength of light, one
can calculate the energy in
one photon, or packet, of
that light:
c = 
E = h
Electronic
Structure
of Atoms
The Nature of Energy
Another mystery
involved the
emission spectra
observed from
energy emitted by
atoms and
molecules.
Electronic
Structure
of Atoms
The Nature of Energy
• One does not observe
a continuous
spectrum, as one gets
from a white light
source.
• Only a line spectrum of
discrete wavelengths
is observed.
Electronic
Structure
of Atoms
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
1. Electrons in an atom can only
occupy certain orbits
(corresponding to certain
energies).
Electronic
Structure
of Atoms
The Nature of Energy
•
Niels Bohr adopted Planck’s
assumption and explained
these phenomena in this
way:
2. Electrons in permitted orbits
have specific, “allowed”
energies; these energies will
not be radiated from the atom.
Electronic
Structure
of Atoms
The Nature of Energy
•
Niels Bohr adopted
Planck’s assumption and
explained these
phenomena in this way:
3. Energy is only absorbed or
emitted in such a way as to
move an electron from one
“allowed” energy state to
another; the energy is
defined by
E = h
Electronic
Structure
of Atoms
The Nature of Energy
The energy absorbed or emitted
from the process of electron
promotion or demotion can be
calculated by the equation:
E = −RH (
1
1
- 2
nf2
ni
)
where RH is the Rydberg
constant, 2.18  10−18 J, and ni
and nf are the initial and final
energy levels of the electron. Electronic
Structure
of Atoms
What does the sign of ΔE
represent?
Electronic
Structure
of Atoms
• ΔE>0
A photon was absorbed
• ΔE<0
Photons are emitted
Electronic
Structure
of Atoms
The Rydberg Equation can be
used to find the wavelength of
an a photon emitted
Electronic
Structure
of Atoms
Example Calculation
• Calculate the energy required to excite
the hydrogen electron from level n = 1
to level n=2. Then, calculate the
wavelength of light that must be
absorbed by a hydrogen atom in its
ground state to reach this excited state.
Electronic
Structure
of Atoms
Example Calculation Answer
• Δ E = 1.635 x 10-18 J
• λ = 1.22 x 10-7 m
Electronic
Structure
of Atoms
What are some of the
limitations of the Bohr model?
Electronic
Structure
of Atoms
The Wave Nature of Matter
• Louis de Broglie posited that if light can
have material properties, matter should
exhibit wave properties.
• He demonstrated that the relationship
between mass and wavelength was
h
 = mv
Electronic
Structure
of Atoms
The Uncertainty Principle
• Heisenberg showed that the more precisely
the momentum of a particle is known, the less
precisely is its position known:
(x) (mv) 
h
4
• In many cases, our uncertainty of the
whereabouts of an electron is greater than the
size of the atom itself!
Electronic
Structure
of Atoms
Quantum Mechanics
• Erwin Schrödinger
developed a
mathematical treatment
into which both the
wave and particle nature
of matter could be
incorporated.
• It is known as quantum
mechanics.
Electronic
Structure
of Atoms
Equations Summary
c = 
h
 = mv
E = h
E = −RH (
1
1
- 2
nf2
ni
)
(x) (mv) 
h
4
Electronic
Structure
of Atoms
Calculations Practice
Complete the worksheet.
Problems not completed in class
are to be completed for
homework.
Electronic
Structure
of Atoms
Closure
• Write the set of 4 quantum numbers for
the last electron in N.
Electronic
Structure
of Atoms