Transcript The energy

CHAPTER 10
ELECTRONS IN
ATOMS
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Waves and Energy
I. Discrepancies with the
Rutherford Model
 All the positive charge is
in the nucleus.
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Waves and Energy
What keeps the nucleus
together?
 The electrons circle the
nucleus.
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Waves and Energy
–Why don’t they spiral into the
nucleus?
» Rutherford’s Model is unstable.
» Niels Bohr
–“Small particles don’t behave
like big particles.”
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Waves and Energy
» So
how do small particles
behave?
» Led to the development of a
new set of rules (mechanics)
to describe these
observations. Quantum
Mechanics by Erwin Schrodinger
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Waves and Energy
 Light
» What
is light?
–A form of energy.
–A source of color
–Fast: 186,000 mi/s (3.0 X
108 m/s)
–Travels through a vacuum.
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Waves and Energy
o
There are two ways for energy
to travel from place to place.
o Particle
is matter
(Remember a particle
o Wave
o
Which is light?
wave
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(A) Refers to node (peak) of
wave. The top peak is the
crest, and the bottom peak is
the trough
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B. Refers to lambda () or
wavelength of wave. The
wavelength is a repeating value.
(C) Refers to amplitude (A) (height)
of peaks.
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Wave Motion (Ocean Analogy)
As the wave
moves past a
stationary
object (bird),
it is not
moved by the
wave itself
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Waves and Energy
Wavelength () (lambda):Distance
between two similar points on
consecutive pulses.
Frequency (): The number of
wavelengths that pass a specific
point per unit of time. (cycles
per second - cps) 1 cps = 1 hertz
(hz)
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Waves and Energy
Amplitude (A): The distance
from rest to crest.
(Maximum disturbance)
Relates to the amount of
energy carried.
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Waves and Energy
»
Visible Light: A portion of the
electromagnetic energy spectrum (em
wave), order of magnitude 1014.
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

Long Wavelength = Low
Frequency = LOW
ENERGY
Short Wavelength =
High Frequency = HIGH
ENERGY
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Waves and Energy
»
How much energy does light carry?
– Max Planck (1900): Determined that
energy was directly related to
frequency
E
»
= h
h = 6.63 X 10-34 j/s
Units of light: PHOTON
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


E = h
E = Energy, in units of Joules (kg·m2/s2)
h = Planck’s constant (6.626 x 10-34
J·s)
  = frequency, in units of hertz (hz,

sec-1)
The energy (E ) of electromagnetic
radiation is directly proportional to
the
frequency () of the radiation.
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Waves and Energy
– Described by Einstein as “wave
packets”.
– Carries a discrete amount of
energy (quantum)
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Waves and Energy
»
Spectrograph:
– Analysis of light using a
spectroscope which breaks light
into component frequencies.
– Continuous Spectrum
 Each color = specific freq &
energy. Light is quantized.
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Spectroscopic analysis of the visible spectrum…
produces all of the colors in a continuous
spectrum
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Waves and Energy
– Bright Line Spectrum
 Each line = a color = a
frequency = an energy value.
 The spectrum is
characteristic of the element.
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Spectroscopic analysis of the hydrogen
spectrum… …produces a “bright line” spectrum
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The Hydrogen Atom

Hydrogen: The simplest atom. It
contains only one electron and
produces the simplest line spectrum.
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The Hydrogen Atom

Observations from spectrum:
» The H atom emits light when
placed in a gas discharge tube.
» The light produces a wellordered spectrum with systematic
spacing.
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The Hydrogen Atom
Each line represents a specific
frequency and energy value.
» No value of E exceeds the
ionization energy of Hydrogen
– Eioniz = energy needed to remove
1 electron
»
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The Hydrogen Atom
– Eioniz = H -> H+ + e-
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The Hydrogen Atom
– Eioniz = H -> H+ + e– Eioniz = 1312 kj
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The Hydrogen Atom
– Eioniz = H -> H+ + e– Eioniz = 1312 kj
 Interpretations
» Hydrogen before becoming excited
has a certain energy condition.
» After ionization, the hydrogen ion
has a certain energy condition.
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The Hydrogen Atom
»
If the H+ recaptures the electron
the PE (potential energy) is
returned to us in the form of
light of frequency  (nu).
– ∆E = Ef - Ei = h
» The ∆E observed is always less
than 1312 kj.
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The Bohr Atom


The hidden staircase.
The Bohr Model
» The spectrum is produced without
losing the electron.
» Accepts Rutherford nucleus
» e- arrangement is dependent upon the
energy condition of the atom. (Energy
of the e- is quantized)
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This produces bands
of light with definite
wavelengths.
Electron transitions
involve jumps of
definite amounts of
energy.
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The Bohr Atom
Only certain “energy levels” are
possible. (Stationary States)
– Ground state: (n=1), the e- can
reside here indefinitely.
– Excited states: (n=2,3,4,. . )
» Changes in levels: Requires energy (up)
or releases energy as light (down).
»
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The Bohr Atom
– Orbital:
 The region of space around a
nucleus in which an electron most
likely will be found.
 An orbital is a region within an atom
where there is a probability of
finding an electron.
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This is a probability diagram for the s orbital in the first
energy level…
Orbital shapes are defined as the surface that
contains 90% of the total electron probability.
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




Quantum Numbers
Each electron in an atom has a unique set
of 4 quantum numbers which describe it.
n=Principal quantum number
M=Angular momentum quantum number
L=Magnetic quantum number
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
Principal Quantum
Number
Generally symbolized
by n, it denotes the
shell (energy level) in
which the electron is
located.
 Number of electrons
that can fit in a shell:
 2n2

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Quantum Numbers: four numbers used
to describe the electrons in an atom.
The Bohr model
• one-dimensional model
• used one quantum number to
describe the electrons
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• Only the size of the orbit was
important, which was
described by
the n quantum number.
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Erwin Schrodinger described an
atomic model with electrons in three
dimensions. This model required
three coordinates, or three quantum
numbers, to describe where electrons
could be found.
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1. Principal (shell) quantum number - n
Describes the energy level within the
atom.
* Energy levels are 1 to 7
•Maximum number of electrons in n is
2n2
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2. Momentum (subshell) quantum number
- l
Describes the sublevel in n
*
Sublevels in the atoms of the known
elements are s - p - d - f
*
Each energy level has n sublevels.
*
Sublevels of different energy levels
may have overlapping energies.
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The Bohr Atom
Wave Functions: Solutions to the
wave equation.
If n = 1, 12 solutions; 1 Orbital
If n = 2, 22 solutions; 4 Orbitals
If n = 3, 32 solutions; 9 Orbitals
If n = 4, 42 solutions; 16 Orbitals
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The Bohr Atom
n=1, 1 orbital; (1)1s
n=2, 4 orbitals; (1)2s, (3)2p
»
(2px,2py,2pz)
n=3, 9 orbitals;(1)3s, (3)3p,(5) 3d
n=4, 16 orbitals; (1)4s, (3)4p,
(5) 4d, (7)4f.
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Orbital filling table
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
Principal Quantum
Number
Generally symbolized by
n, it denotes the shell
(energy level) in which
the electron is located.
 Number of electrons that
can fit in a shell:
 2n2

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Sizes of s orbitals
Orbitals of the same shape (s, for instance) grow
larger as n increases…
Nodes are regions of low probability within an
orbital.
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The Bohr Atom
Wave Functions: Solutions to the
wave equation.
If n = 1, 12 solutions; 1 Orbital
If n = 2, 22 solutions; 4 Orbitals
If n = 3, 32 solutions; 9 Orbitals
If n = 4, 42 solutions; 16 Orbitals
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generally symbolized by l, denotes the orbital
(subshell) in
which the electron is located.
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The s orbital has a spherical shape centered
around
the origin of the three axes in space.
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Magnetic Quantum Number
The magnetic quantum number, generally symbolized
by m, denotes the orientation of the electron’s
orbital with respect to the three axes in space.
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Things get a bit more
complicated with the
five d orbitals that are
found in the d sublevels
beginning with n = 3. To
remember the shapes,
think of “double
dumbbells” …and a
“dumbbell with a donut”!
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