Download Arrangement of Electrons in Atoms (Chapter 4) Notes

Arrangement of Electrons in
Atoms (Chapter 4) Notes
Part 1 Properties of Electrons
I. Properties of Light-Different types of
electromagnetic radiation (x-rays, radio
waves, microwaves, etc…) SEEM to be
very different from one another. Yet
they share certain fundamental
characteristics. All types of
electromagnetic radiation, also called
radiant energy, move through a vacuum
at a speed of 3.00 x l08 meters per
second.
A. Wavelength – distance between
identical points on successive waves;
may be measured in any length unit but
is usually dependent on how long the
wave is (X-rays are usually measured in
nanometers or Angstroms while the very
long radio waves might be measured in
meter. The Greek letter, , is used to
depict wavelength (pg 92)
B. Frequency – the number of complete wave
cycles that pass a given point in one second:
the unit is cycles/second but is written as sec-1,
or Hertz. The Greek letter , is used to depict
frequency.
Wavelength and frequency vary inversely and are
thus related as the product of frequency and
wavelength equals the speed of light, c.
c =
c = 3.00 X 108m/s
1.
What is the wavelength of radiation whose frequency is
6.24 x l013 sec-1?
2.
A: 4.81X10-6 m
what is the frequency of radiation whose wavelength is
2.20 x l0-6 nm? (2.20 X 10-15 m)
3.
A: 1.36X1023 s-1 or Hz
The range of visible light is generally considered to be
from 350 to 700 nm (3.50 X 10-7m to 7.00 X 10-7 m. What
is the range of frequency of visible light?
A: 8.6X1014 s-1or Hz to 4X1014 s-1or Hz
Violet:
Indigo:
Blue:
Green:
Yellow:
Orange:
Red:
400 - 420 nm
420 - 440 nm
440 - 490 nm
490 - 570 nm
570 - 585 nm
585 - 620 nm
620 - 780 nm
When white light passes through or is reflected by a
colored substance, a characteristic portion of the
mixed wavelengths is absorbed. The remaining light
will then assume the complementary color to the
wavelength(s) absorbed. This relationship is
demonstrated by the color wheel shown on the right.
Here, complementary colors are diametrically
opposite each other. Thus, absorption of 420-430 nm
light renders a substance yellow, and absorption of
500-520 nm light makes it red
II. The Photoelectric Effect (pg 93) – refers to the
emission of electrons from a metal when light
shines on the metal. The wave theory of light (early
1900) could not explain this phenomenon. The
mystery of the photoelectric effect involved the
frequency of the light striking the metal. For a
given metal, no electrons were emitted if the light’s
frequency was below a certain minimum –
regardless of how long the light was shone. Light
was known to be a form of energy, capable of
knocking loose an electron from a metal. But the
wave theory of light predicted that light of any
frequency could supply enough energy to eject an
electron. Scientists couldn’t explain why the light
had to be of a minimum FREQUENCY in order for
the photoelectric effect to occur.
Energy Information – Radiation of different
wavelengths affect matter differently – certain
wavelengths (near infrared) may burn your skin
with a heat burn, overexposure to X radiation
causes tissue damage. These diverse effects are
due to differences in the energy of the radiation.
Radiation of high frequency and short wavelength
are more energetic than radiation of lower
frequency and longer wavelength. THE
QUANTITATIVE RELATIONSHIP BETWEEN
FREQUENCY AND ENERGY WAS DEVELOPED
THROUGH THE QUANTUM THEORY OF MAX
PLANCK.
The explanation of the photoelectric effect dates
back to 1900 when Max Planck revised classical
ideas of light by proposing that light, which before
was thought of as a collection of waves, consisted
of BUNDLES OF ENERGY called QUANTA. A
quantum is the minimum quantity of energy that
can be lost or gained by an atom. Planck
proposed the following relationship between a
quantum of energy and the frequency of radiation:
E = hv
Planck’s constant, h, is 6.63 x l0-34 Joules  sec
Many times, you will use this formula AND the
formula, c = , together.
1.
b.
2.
3.
4.
If a certain light has 7.18 x l0-19 J of energy, what is
the frequency of this light?
A: 1.08X1015 s-1or Hz
what is the wavelength of this light?
A: 2.75X10-7 m
If the frequency of a certain light is 3.8 x l014 Hz,
what is the energy of this light?
A: 2.5X10-19 J
The energy of a certain light is 3.9 x l0-19 J. What is
the wavelength of this light? Is it visible?
A: 510 nm – Yes visible light.
Calculate the smallest increment of energy that an
object can absorb from yellow light, the color given
off when sodium atoms are heated in a flame. The
wavelength of this light is 589 nm.
A: 3.36X10-19 J
Albert Einstein expanded on Planck’s theory
by explaining that electromagnetic radiation
has a dual wave-particle nature. While light
exhibits many wavelike properties, it can
also be thought of as a stream of particles.
Each particle of light carries a quantum of
energy. Einstein called these particles
PHOTONS. A photon is a particle of
electromagnetic radiation having zero mass
and carrying a quantum of energy.
Einstein explained the photoelectric effect by
proposing that electromagnetic radiation is
absorbed by matter only in whole numbers of
photons. In order for an electron to be ejected
from a metal surface, the electron must be struck
by a single photon possessing at least the
minimum energy (Ephoton = hv) required to knock
the electron loose, this minimum energy
corresponds to a minimum frequency. If a
photon’s frequency is below the minimum, then
the electron remains bound to the metal surface.
Electrons in different metals are bound more or
less tightly, so different metals require different
minimum frequencies to exhibit the photoelectric
effect.
Example from problem 4: An atom or
molecule emitting or absorbing radiation
whose wavelength is 589 nm cannot
lose or gain energy by radiation except
in MULTIPLES OF 3.37x l0-19 J. It
cannot, for example, gain 5.00 x l0-19 J
from this radiation because this amount
is not a multiple of 3.37 x l0-19.
In astronomy, it is often necessary to be able to detect
just a few photons because the light signals from distant
stars are so weak. A photon detector receives a signal of
total energy 4.05 x l0-18 J from radiation of 540 nm
wavelength. How many photons have been detected?
A: 11 photons
5.
Excited chromium atoms strongly emit radiation of 427
nm. What is the energy in kilojoules per photon?
A: 4.66X10-22 kJ
6.
7. Light hitting certain chemical substances may cause
rupture of a chemical bond. If a minimum energy of 332
kJ is required to break a carbon-chlorine bond in a plastic
material, what is the longest wavelength of radiation that
possesses the necessary energy? A: 5.99X10-31 m
III. The Hydrogen-Atom Line-Emission
Spectrum
When investigators passed electric current
through a vacuum tube containing hydrogen
gas at low pressure, they observed the
emission of a characteristic pinkish glow.
When a narrow beam of the emitted light was
shined through a prism, it was separated into
a series of specific frequencies (and therefore
specific wavelengths, c =) of visible light.
The bands of light were part of what is known
as hydrogen’s LINE-EMISSION SPECTRUM.
(page 95)
The lowest energy state of an atom is its
ground state.
A state in which an atom has a higher
amount of energy is an excited state.
When an excited atom returns to its
ground state, it gives off energy.
IV. Bohr’s Model of Hydrogen – Neils Bohr
incorporated Planck’s quantum theory to
explain line-emission spectra. Bohr said the
absorptions and emissions of light by
hydrogen corresponded to energy changes
within the atom. The fact that only certain
frequencies are absorbed or emitted by an
atom tells us that only certain energy
changes are possible.
Bohr’s model incorporated (l) Rutherford’s
Experiment, which established a nucleus and
(2) Einstein’s theory that used Planck’s
quantum theory to determine that light is
discrete bundles of energy.
V. Bohr’s Theory of the Atom:
Electrons cannot have just any energy; only
orbits of certain radii having CERTAIN
energies are permitted.
Thus, when an electron absorbs quanta of
energy, it will cause them to jump away from
the nucleus to a higher orbit (energy level or
n) and when the electron falls from a high
orbit to a lower one, a photon of a particular
wavelength is released, and a particular color
will be given off. Bohr was able to calculate a
set of allowed energies. Each of these
allowed energies corresponds to a circular
path of a different radius.
Thus the larger the value of n, the farther the
electron is from the nucleus and the higher
energy it possesses.
The success of Bohr’s model of the hydrogen
atom is explaining observed spectral lines led
many scientist to conclude that a similar
model could be applied to all atoms. It was
soon recognized, however, that Bohr’s
approach did not explain the spectra of atoms
with more than one electron. Nor did Bohr’s
theory explain the chemical behavior of
atoms.
Part 2 Quantum Model of the
Atom
So, where are the electrons of an atom
located?
A. Various Models of the Atom
Dalton’s Model
Thompson’s Plum Pudding Model
Rutherford’s Model
Bohr’s ‘Solar System’ Model – electrons rotate around the
nucleus
Quantum Mechanics Model – modern description of the
electron in atoms, derived from a mathematical equation
(Schrodinger’s wave equation)
B. In 1926, the Austrian physicist Erwin Schrodinger
used the hypothesis that electrons have a dual
wave/particle nature to develop an equation that
treated electrons in atoms as waves.
Schrodinger’s equation results in a series of so
called wave functions, represented by the letter 
(psi). Although  has no actual physical meaning,
the value of 2 describes the probability
distribution of an electron. (Same concept you
learned in Algebra II when you were doing linear
regressions and finding the best fit line.)
We cannot know both the location and
velocity of an electron (Heisenberg’s
uncertainty principle), thus
Schrodinger’s equation does not tell us
the exact location of the electron, rather
it describes the probability that an
electron will be at a certain location in
the atom.
1.
Waves are confined to a space and can
only have certain frequencies.
2.
Electrons are considered to be waves
confined to the space around an atomic
nucleus. Electrons can only exist at specific
frequencies. And according to E=hv
(Planck’s hypothesis), these frequencies
correspond to specific energies (or quantified
amounts of energy.)
3.
Electrons, like light waves, can be bent or
diffracted.
Heisenberg’s Uncertainty Principle: says that
there is a fundamental limitation on just how
precisely we can hope to know both the location
and the momentum of a particle. It turns out
that when the radiation used to locate a particle
hits that particle, it changes its momentum.
Therefore, the position and momentum cannot
both be measure exactly. As one is measured
more precisely, the other is known less
precisely.
Today we say that the electrons are located in a
region outside the nucleus called the
electron cloud.
C.
I.
Electron Cloud – Energy Levels
Electrons are found in various energy levels
around the nucleus. The energy levels are
analogous to the rungs of a ladder. The lowest
rung of the ladder corresponds to the lowest
energy level. A person can climb up or down a
ladder by going from rung to rung. Similarly, an
electron can jump from one energy level to
another. A person on a ladder cannot stand
between the rungs, similarly, the electrons in an
atom cannot exist between energy levels.
A. Quantum: To move from one rung to
another, a person climbing a ladder
must move just the right distance. To
move from one energy level to another,
an electron must gain or lose just the
right amount of energy. The exact
amount of energy required to move from
one energy level to another is called a
quantum of energy.
B. Photon: When electrons move from
one energy level to another energy level
we see light – going from one energy
level to another energy level gives off
an exact amount of light (called a
photon).
II. Quantum Mechanics Model of the Atom and
Quantum Numbers
Quantum Numbers – a series of numbers which
describe several properties of an energy level (or
orbit)
A. Principal Quantum Number, “n” (Energy
Levels): energy levels (represented by the letter
n) are assigned values in order of increasing
energy: n=1,2,3,4, and so forth…. which
correspond to the periods in the periodic table.
The principle q. n. is related to the size and
energy of the orbital. n=1, n=2, n=3, n=4, n=5,
etc… Which energy level is furthest away from
the nucleus and has electrons with the highest
energy - 1, 2,3, or 4?
B. Angular Momentum or Azimuthal
Quantum Number, “l” (Sublevels):
Within each energy level, the electrons
are located in various sublevels – there
are 4 different sublevels s, p, d, and f.
“l” defines the shape of the orbital (s, p,
d, & f). The possible values of “l” are
limited by the value for “n”. If n = 3, “l”
can be 0, 1, or 2, but not 3 or higher.
This q.n. is related to the shape of the
orbital.
l = 0, is referring to the s sublevel
l = 1, is referring to p sublevel
l = 2, is referring to d sublevel
l = 3, is referring to f sublevel
1s
2s
2p
3p
C. Orbital’s: Where are the electrons
in the various sublevels located in
relation to the nucleus? Electrons
are NOT confined to a fixed circular
path, they are, however, found in
definite regions of the atoms – these
regions are called atomic orbital’s!
Each orbital can only hold 2 electrons at
a time (Pauli exclusion principle).
Within the s sublevel (l=0) there is only 1
orbital (which is spherical) it is called the s
orbital.
http://www.shef.ac.uk/chemistry/orbitron/AOs/1s/index.html
Within the p sublevel (l=1) there are 3
orbital’s (which are dumbbell shaped)
called the px, py, pz orbital’s.
Within the d sublevel (l=2) there are 5
orbital’s (4 of which are cloverleaf shaped)
called the dxy, dxz, dyz, dx2-y2, dz2 orbital’s.
Within the f sublevel (l=3) there are 7
orbital’s - which are too complex to draw
The magnetic quantum number, ml,
refers to the position of the orbital
(plane) in space relative to other
orbital’s. It may have integral numbers
ranging from 0 in the s sublevel, 1 to –1
in the p sublevel, 2 to –2 in the d
sublevel and 3 to –3 in the f sublevel.
ml = 0, is referring to the s orbital
ml = -1, 0, +1, are referring to the three
p orbital’s (px, py, and pz)
ml = -2, -1, 0, +1, +2, are referring to the
five d orbital’s
ml = -3, -2, -1, 0, +1, +2, +3, are
referring to the seven f orbital’s
Examples:
What are the values of n, l, and ml for the
orbital’s in the 3 d sublevel?
2. What are all possible values of n, l, and
ml in the n = 3 energy level?
3. Which of the following sets of quantum
numbers are NOT allowed in an atom? For
each incorrect set, state why it is incorrect.
A. n = l, l = 0, ml = l
B. n = 2, l = 2, ml = l
C. n = 5, l = 3, ml =2
D. n = 6, l = -2, ml =2
E. n = 6, l = 2, ml = -2
D. How many electrons can go into
each energy level?
Each orbital can hold two electrons. (2n2
= number of electrons per energy level)
D.
The 1st energy level (n=1) only has 1
sublevel called 1s. s only has 1 orbital
called the s orbital, so only 2 electrons will
be found in the 1st energy level. (2n2 = 2)
The 2nd energy level (n=2) has 2
sublevels called 2s and 2p. s only has
1 orbital called the s orbital, p has 3
orbital’s called px, py, and pz orbital’s,
so 8 electrons will be found in the 2nd
energy level. (2n2 = 8)
The 3rd energy level (n=3) has 3
sublevels called 3s, 3p, and 3d. s only
has 1 orbital called the s orbital, p has 3
orbital’s called px, py, and pz orbital’s,
and d has 5 orbital’s, so 18 electrons
will be found in the 3rd energy level.
(2n2 = 18)
How about the 4th energy level?
It has 4 sublevels called 4s, 4p, 4d, and
4f. s only has 1 orbital, p has 3 orbital’s,
d has 5 orbital’s, and f has 7 orbital’s, so
32 electrons will be found in the 4th
energy level. (2n2 = 32)
E. Lets put it all together:
Example of neon atom:
Fourth Quantum Number, ms, refers to the
magnetic spin of an electron within an
orbital. Each orbital can hold two electrons,
both with different spins. Clockwise spin is
represented with a value of +1/2 and
counterclockwise spin is represented with a
value of –1/2. Electrons fill the orbital’s one
at a time with the same spin (+1/2), then fill
up the orbital(s) with electrons of the opposite
spin (-1/2).
ms = +1/2 or –1/2
Example: Which of the following sets of
quantum numbers are not allowed?
For each incorrect set state why it is
incorrect.
A. n = 3, l = 3, ml = 0 ms = -1/2
B. n = 4, l = 3, ml = 2, ms = -1/2
C. n =4, l = l, ml = l, ms = +1/2
D. n = 2, l – 1, ml = -l, ms = -1
E. n = 3, l = 1, ml = -2, ms = -1/2
Quantum Numbers Analogy
Energy Levels (n) or Principal Q.N.
n=1 (Georgetown)
n=2 (Austin)
n=3 (San Antonio) n=4 (Laredo)
Sublevels (l) or Azimuthal Q.N.
l=0 – s shape 1 bedroom
l=1 – p shape 3 bedroom
l=2 – d shape 5 bedroom
l=3 – f shape 7 bedroom
Orbital’s (ml) or Magnetic Q.N.
If l=0 then ml=0 (Represents the 1 bed/orbital in the s sublevel)
If l=1 then ml= -1, 0, 1 (Represents the 3 bed’s/orbital’s in the p
sublevel)
If l=2 then ml= -2, -1, 0, 1, 2 (Represents the 5 bed’s/orbital’s in the p
sublevel)
If l=3 then ml= -3, -2, -1, 0, 1, 2, 3 (Represents the 7 bed’s/orbital’s in
the p sublevel)
Magnetic Spin – Fourth Q.N. (ms)
ms = +1/2 - 1st electron in orbital
ms = -1/2 – 2nd electron in orbital
Part III: Electron
Configurations
I. Electron Configuration:
Definition of electron configuration: An
electron configuration is a written
representation of the arrangement of
electrons in an atom.
Rules for writing Electron
Configurations:
Aufbau Principle – electrons fill
in order from lowest to highest
energy.
Aufbau Diagram
The Pauli Exclusion Principle – An orbital
can only hold two electrons.
Two electrons in the same orbital must have
opposite spins.
How many electrons can occupy each sublevel
(s, p, d, f)?
s = 1 x 2 = 2 ep = 3 x 2 = 6 ed = 5 x 2 = 10 ef = 7 x 2 = 14 e-
Hund’s rule – the lowest energy
configuration for an atom is the one
having the maximum number of
unpaired electrons for a set of
degenerate orbital’s. By convention, all
unpaired electrons are represented as
having parallel spins with spin “up”.
Hund’s Rule
One electron enters each orbital until all
the orbitals contain one electron with
spins parallel.
Ex. Nitrogen
1s
2s
2p
II.
What? How do we write an electron
configuration?
1st rule - electrons occupy orbital’s that require
the least amount of energy for the electron to
stay there. So always follow the vertical rule
(Aufbau Principle):
You notice, for example, that the 4s sublevel
requires less energy than the 3d sublevel;
therefore, the 4s orbital is filled with electrons
before any electrons enter the 3d orbital!!!! So
just follow the above chart and you can’t go
wrong!!!!)
A.
Diagonal Rule
B. 2nd rule – only 2 electrons can go into
any orbital, however, you must place
one electron into each orbital in a
sublevel before a 2nd electron can
occupy an orbital. Orbital’s with only 1
electron in the orbital are said to have
an unpaired electron in them.
III. Writing Electron
Configurations (3 ways):
A. Orbital Notation: an unoccupied
orbital is represented by a line______,
with the orbital’s name written
underneath the line. An orbital
containing one electron is written as
_____, an orbital with two electrons is
written as ____. The lines are
labeled with the principal quantum
number and the sublevel letter.
Examples:
(Remember that you must place
one electron into each orbital before a second
electron in placed into an orbital.)
Hydrogen ____
Helium __
1s
1s
Lithium ___ ____
1s
2s
Carbon ____ ____ ____ ____ _____
1s
2s
2p
2p
2p
You try to write the notation for Titanium
B. Electron Configuration Notation:
eliminates the lines and arrows of orbital
notation. Instead, the number of
electrons in a sublevel is shown by
adding a superscript to the sublevel
designation. The superscript indicates
the number of electrons present in that
sublevel.
Examples:
Hydrogen: 1s1
Helium: 1s2
Lithium: 1s22s1
Carbon: 1s22s22p2
You try to write the notation for
Titanium
C.
Short Hand or Noble Gas Notation:
Use the noble gases that have complete
inner energy levels and an outer energy
level with complete s and p orbital’s. Use
the noble gas that just precedes the
element you are working with.
Boron is ls22s22p1
The noble gas preceding Boron is He, so the
short way is [He]2s22p1.
Sulfur is ls22s22p63s23p4
Short way: [Ne]3s23p4
Example: Titanium
Using the Periodic Table
More Practice Problems:
Write electron configurations for each of the following
atoms:
1. boron
2. sulfur
3. vanadium
4. iodine
Draw orbital diagrams for these:
5. sodium
6. phosphorus
7. chlorine
Write shorthand electron configuration for the following:
8. Sr
9. Mo
10. Ge
IV.
Electron Configurations and Quantum Numbers –
When writing the quantum numbers for a given
element, keep the following in mind:
1. The highest energy electron is the LAST one you write
in the electron configuration.
1s22s22p63s23p5 -- the 3p5 electron is the last
written. Remembering Aufbau’s Principle, electrons fill
from the lowest to the highest energy.
2. The outermost electron is the one with the LARGEST
principle quantum number. It may be the last one
you write: 1s22s22p63s23p64s23d104p2. The 4 p2 is the
farthest from the nucleus. OR
(2) 1s22s22p63s23p64s23d10. Here, it is the 4s2 electron,
because it has the largest principle q.n.
To write the quantum numbers for the first
example above, the 3p5 electron:
n = 3, l = 1, ml = 0, ms = -1/2
For the second example, the 4p2 electron:
n = 4, l = 1, ml = 0, ms = +1/2
For the third example, the 4s2 electron is the
outermost electron (but not the one with the
highest energy) so the q.n.’s for the
outermost electron would be:
n = 4, l = 0, ml = 0, ms = -1/2
You try it: Write the electron configuration
and the quantum numbers for the
following:
1. outermost electron in bromine
2. outermost electron in copper
3. highest energy electron in vanadium
4. Write the electron configuration and the
quantum numbers for the 35th electron in
rubidium
Irregular Electron configurations –
sometimes the electron configuration is
NOT what we would predict it to be.
Sometimes electrons are moved
because (l) it will result in greater
stability for that atom or (2) for some
unknown reason??
It is very important to define “stable” here.
STABLE means:
1. all degenerate (equal energy) orbital’s are
FULL
2. all degenerate orbital’s are half-full
3. all degenerate orbital’s are totally empty.
Examples – draw the orbital’s (lines or boxes) and
fill each orbital with the predicted number of
electrons. Predict the electron configuration for Cr
#24: [Ar]4s23d6
However, the real E. C. is [Ar]4s13d5. The 4s1
electron has been moved to achieve greater
stability.
ALWAYS USE THE ACTUAL E. C. AND NOT THE
PREDICTED ONE. YOU WILL HAVE THESE
ATOMS WITH IRREGULAR E. C. HIGHLIGHTED
OR MARKED ON YOUR PERIODIC TABLE.
Electron configurations for Ions-First,
determine if the element will lose or gain
electrons. Secondly, what number of
electrons will be gained or lost? It is
recommended that you write the e.c.
for the atom and then determine what
will happen.
For cations (positive ions) – look at the element
and decide how many electrons will be lost when
it ionizes and keep that in mind when writing the
E. C. The last number in the E. C. will now be
LESS than what is written on your periodic table.
Ex. Write the electron configuration for
magnesium ion: [Ne]3s2 is for the atom. Mg is a
metal and will lose its valence (outer) electrons,
so the e.c. for Mg2+ is 1s22s22p6
Practice:
1. #3
2. #12
3. #19
4. #13
For anions (negative ions) – look at the element
and decide how many electrons that element will
GAIN when it ionizes. The last number in the E.
C. will be MORE than what is written on the
periodic table.
Ex. Sulfide ion: Sulfur atom is 1s22s22p4. Sulfur
is a nonmetal with 6 valence electrons (2s2 and
2p4) and will gain 2 electrons: 1s22s22p6 is for the
sulfide ion.
Practice:
1. #17
2. #7
3. #16
4. #30