Download Chapter 7: Quantum Theory and the Electronic Structure of Atoms

Chapter 7: Quantum Theory and the Electronic Structure
of Atoms
Atomic Structure Revisited (Sections 7.1 - 7.2)
Bohr’s Theory of the Hydrogen Atom (Section 7.3)
The Dual Nature of the Electron (Section 7.4)
Quantum Mechanics and Quantum Numbers (Sections 7.5 - 7,7)
Electron Configurations and the Aufbau Principle (Sections 7.8 - 7.9)
SUMMARY
Atomic Structure Revisited (Sections 7.1 - 7.2)
The experiments conducted to study the structure of atoms at the end of the
nineteenth and beginning of the twentieth centuries were described in Chapter 2. The
results of these experiments depict an atom with an exceedingly small, positively charged
nucleus surrounded by negative electrons. When scientists attempted to interpret the
results of these experiments using the accepted theories of the day, such as Newton’s laws
of motion and Maxwelrs electromagnetic wave theory of radiation, they did not have much
success. For example, it was well known that the wavelength of radiation emitted by hot
solids decreases with increasing temperature, but the correlation could only be predicted for
either short or long wavelengths. The results of other experiments couldn’t be predicted at
all. The same theory that postulated that atomic stability required electrons to be in motion,
predicted that electrons moving in the electric field of the positive nucleus would emit
radiation, lose energy and quickly collapse onto the nucleus. On the basis of the same
theory, gases subjected to electric fields in discharge tubes were expected to emit a
continuous range of energies, but they emit narrow bands of radiation (selected
wavelengths) instead. Equally perplexing results were observed in a very different
experiment involving metals. When metals were irradiated by some frequencies of light,
electrons were ejected from the metal surface. This was called the photoelectric effect.
Efforts to correlate the incidence and rate of electron ejection to the properties of the
radiation u~ing nineteenth century physics were futile.
The solution to all of these problems started with the work of Max Planck in 1990.
Planck successfully described the entire wavelength range of radiation emitted by hot solids
by constraining energy to be absorbed and emitted in discrete packets called quanta. A
single quantum of energy is defined as proportional to the frequency, v (nu), of the radiation
The importance of the idea that energy is transferred in quanta was reinforced in 1905 by
the work of Albert Einstein, which established that electromagnetic radiation exists as
quanta. This ’~as a great surprise because a staggering amount of work confirmed the fact
that electromagnetic radiation consists of mutually perpendicular, oscillating electric and
magnetic fields, i.e. waves. The distance between the maxima in the waves is called the
wavelength, x (lambda). Remember, the Sl unit for distance is the meter (m), though it is
more common for wavelengths to be reported in nanometers (rim). The frequency of a wave
is the number of crests (or troughs) that pass a fixed point per second. The unit of
frequency is cycles per second which is written as/s or s-1. The Sl unit for frequency is the
127
128 Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms
hertz (Hz). The product of the wavelength and the frequency of any wave is theExample
velocity or speed of the wave, usually in meters per second. All electromagnetic 7.1
waves travel at the same ,s~eed through a vacuum. This speed, known as the
speed of light, is 3.00 x 10 m/s and has the symbol c:
Exercises
7-1 - 7-5
Long wavelength radiation, such as radio waves, is low frequency; short wavelength
radiation, such as x-rays, is high frequency. Visible radiation covers a very small range of
wavelengths (400 - 700 rim) in the middle of the infinite electromagnetic spectrum.
In wave theory, the energy carried by an electromagnetic wave (intensity) depends on
the square of the electric field amplitude (height of the wave measured from its midpoint).
This is why the photoelectric effect was impossible to understand before Einstein applied
Plank’s idea of quantized energy to the situation. Electrons are only ejected from surfaces
by radiation with a frequency equal to or greater than some threshold value (the threshold
frequency is different for each metal). According to wave theory, this should not be the
case; it should be possible to increase the amplitude of any wave to a large enough value to
induce electron ejection. What scientists observed was that changing the intensity
(amplitude) of the wave changed the rate of electron ejection only if the radiation frequency
was above the threshold frequency. A very intense radiation below the threshold frequency
would melt the metal rather than induce electron ejection. Each electron is held to the metal
by a force called the binding energy (BE). Einstein realized that if the energy of the radiation
was quantized, the radiation was behaving like a particle that could interact with a single
electron on the metal surface. Today, we call radiation particles photons. According to
Einstein, below the threshold frequency, a photon does not have enough kinetic energy to
overcome the binding energy and eject an electron from the metal surface, but above the
threshold frequency it does. Since the binding energy is constant, as the photon energy
(frequency) increases, more of its energy is available to become kinetic energy (KE) in the
electrons ejected from the metal.
KE = hv - BE
This theory described the experimental results completely, but it was difficult for
scientists to embrace the idea that radiation could behave as waves in some
circumstances and as particles in others. Today, this wave-particle duality is widely
Exercise
accepted and known to apply to all energy, including matter. More on this later.
7-6
Bohr’s Theory of the Hydrogen Atom (Section 7.3)
One of the experimental observations that perplexed scientists at the end of the nineteenth
century was the emission of narrow bands of radiation by gases excited in discharge tubes.
Scientists had known for years that each element emits a unique spectrum (series of
radiation frequencies), but the source of the emission was not understood until 1913 when
Niels Bohr predicted the emission spectrum of the hydrogen atom. Bohr kept the popular
solar system-inspired picture of an electron making a circular orbit around the nucleus, but
restricted the electron to a finite set of orbits, each associated with a specific radius and
energy. When energy is absorbed by the atom, the electron must jump to a higher energy
orbit. The lowest energy configuration occurs when the electron is closest to the nucleus,
when n = 1. This is called the ground state. Hydrogen atoms that have an electron in a
higher energy orbit are called excited state atoms. Bohr was able to calculate the radii of
the allowed orbits and their energies. The energies of the H atom are given by:
Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms 129
R1
the Rydberg constant which has a value equal to 2.18 x 10-is J. The integer n
is a label for each electron orbit and is called the principal quantum number. The minus sign
in the equation does not signify negative energy; it means that the energy of the hydrogen
atom is lower than that of a completely separated proton and electron for which the force of
attraction is zero.
Bohr’s stroke of genius was to equate an energy change of the atom to the energy of a
photon of emitted light. Bohr attributed the lines of the emission spectrum to the radiation
emitted by the atom as the electron drops from a higher energy orbit to a lower energy one
closer to the nucleus. In order for energy to be conserved, the energy lost as radiation must
equal the difference in the energies of the initial and final electron orbits. For the emission
process, Ei and ni (i ~tands for initial) represent the higher atomic energy and larger orbit
radius; nf and Ef (f stands for final) represent the lower energy and smaller radius.
Substituting the expression for each energy level, the change in energy of the atom AEatom
is
where RH is
Since, the energy of a photon is by= hc/,t the wavelengths emitted by the hydrogen atom
are
Examples
7.2, 7.3
The Balmer series is the portion of the hydrogen atom spectrum that falls in the
visible region. It corresponds to transitions to the second energy level of the
hydrogen atom.
Exercises
7-7 - 7-10
The Dual Nature of the Electron (Section 7.4)
Bohr’s theory works for H atoms but fails to predict spectra of any other elements or
even for H2. Moreover, no one, including Bohr, could justify the quantization of electron
orbits or atomic energy levels. In 1924 Louis de Broglie hypothesized that if photons can
have the properties of particles as well as waves, electrons could have the properties of
waves as well as particles! He realized that the "wavelength" of the electron would have to
be a multiple of the orbit circumference to avoid canceling itself out by destructive
interference. De Broglie deduced that the wavelength x of a particle depends on its mass, m,
and velocity, u:
h
Experimental evidence of the wave properties of electrons was provided in 1927 by Example
diffraction experiments. Diffraction is a phenomenon that can be explained only by 7.4
wave motion. Since electrons were observed to produce diffraction patterns, the
electrons were proven to behave as waves. According to de Broglie’s equation, the Exercise
wavelength of a particle increases as its mass decreases, so wave properties are 7-11
130 Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms
significant for atomic and su_b~tomic particles, As the mass of a particle reaches
macroscopic size (say, > 10- g) its wavelength becomes extremely short and wave
properties cannot be observed.
Quantum Mechanics and Quantum Numbers (Sections 7,5 - 7.7)
Werner Heisenberg realized that if a subatomic particle behaves like a wave, it is
impossible to know its position (or lifetime) and momentum (or energy) precisely and
simultaneously, The position of a moving particle is most accurately determined over an
infinitely short time interval. However, it is impossible to describe an infinitely short time
interval using a single frequency. Similarly, the energy of a wave is most accurately
determined when the extent of the wave is infinitely long. The idea of position makes no
sense for an infinitely long wave. The Heisenberg uncertainty principle distills this
relationship to a simple statement:
AxAp = AtAE >_h--,
4~
Erwin Schr6dinger developed a theory for computing electron energies based on the
idea that we don’t have to specify the position or path of the electron in order to compute its
energy and predict spectra. The Schr6dinger equation (SE) is beyond our ability to solve,
but we will use the SE solutions, energies, E, and wave functions ~//, to describe the state of
electrons around the nucleus, The square of a wave function, ~/t, is proportional to the
probability that an electron can be found at specific spatial coordinates around the nucleus.
(The dependence on ~ makes sense when we remember that wave intensity depends on
the square of the amplitude.) The probability that an electron can be found in a particular
region around an atom also is called the electron density.
The solutions of the Schr6dinger equation specify the energy levels and spatial
distributions of the electron in the hydrogen atom. In contrast to the circular orbits of the
Bohr solar model, the wavefunction specifies an atomic orbital, a representation of the
volume an electron can occupy. The Schr6dinger equation has an exact solution for the
hydrogen atom, but can only be solved using approximation methods for atoms with more
than one electron, The approximate methods use the SchrSdinger equation solutions for the
¯ hydrogen atom as approximations for descriptions of electrons in larger atoms.
Each solution of the SchrSdinger equation is specified by the values of three
parameters called quantum numbers. We use the quantum numbers as symbols of the
wavefunctions, the atomic orbitals they represent or the electrons that reside in them.
Principal quantum number, n. The principal quantum number can take any positive
integer value: 1 >__ n > oc. The principal quantum number reflects the average distance
of an electron from the nucleus, All the known elements have n between 1 and 7.
Angular momentum quantum number, L The angular momentum quantum number
can take integer values between zero and (n-1). The angular momentum quantum
number reflects the shape of the electron distribution, (The boundaries of an
electron cloud need not be well defined for an orbital to have an overall shape.)
~ defines a group of orbitals composing a specific sublevel or subshell, The following
table correlates the value of ~ to the letter designation and shape.
Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms 131
letter
0
1
2
s
3
f
P
d
shap~
i spherical
dumbell
crossed
dumbells
multi-lobed
3. Magnetic quantum number, mz. The magnetic quantum number can take integer
values between -~ and [. The number of me values is important because it designates
the number of orbitals within a subshell. For example, when ~ = I, there are three me
values. Consequently, p orbitals always occur in groups of three orbitals. These
three p orbitals all have the same energy, but have different orientations in space
(each aligned with one of the Cartesian axes, for example).
The fourth quantum arises during the extension of the Schr6dinger equation to
many electron atoms. During his effort~ to predict emission spectra, Wolfgang Pauli Examples
proposed a spin quantum number for electrons and later postulated an exclusion
7.5-7.8
principle: no two electrons in an atom can have all four quantum numbers the same.
This principle limits the number of electrons each atomic orbital can hold to no more Exercises
than two electrons. The electron spin quantum number, ms, designates one of two 7-12 - 7-17
possible spin directions for electrons. (Remember that spinning charges induce
magnetic fields.) The two possible values of ms are +1/2 and -1/2.
Electron Configurations and the Aufbau Principle (Sections 7.8 - 7.9)
The energies of all the orbitals in a subshell are the same for a hydrogen atom (with
I electron moving around). The electron density distributions are different for p and s
orbitals, but they have the same energy. In other words, the energies of the orbitals
increase with n:
ls < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f< 5s ...
The energies of orbitals of atoms containing several electrons are shifted by electron
repulsion and electrostatic shielding of the nucleus by the lower energy electrons.
Consequently, the orbital energies depend on n and ~. For example, the energy of an atom
is lower when the 4s orbital is filled before the 3d. The order of the energy levels in many
electron atoms becomes
ls < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4d < 5d ...
With this knowledge, we can write an atomic formula that reflects the energy and distribution
for every electron in every element on the periodic chart. We will see clearly what has been
implied since Chapter 2: the similarity in chemical and physical properties associated with
the elements in a group arise from similarities in the arrangement of the electrons around
the nucleus of those atoms. We call this arrangement the electron configuration. The
ground state electron configuration of H is ls1, as illustrated.
132 Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms
The number of electrons per subshell
Principal electron shell
(value of n)
Type of orbital occupied
The electron configurations of many-electron atoms are constructed by adding an electron
to the next (lowest energy) empty orbital. This is called the Aufbau or building up principle.
So, the electron configuration of He is ls2. The electron configurations of the first five
elements in the first (alkali metals) and eighth (noble gas) groups are
As you can see, the electron configurations for the large elements are long and unwieldy.
The electron configurations of the noble gas elements can be used as abbreviations when
writing electron configurations. Neon has the electron configuration 1s22s22p6. All elements
beyond neon have this configuration for the first 10 electrons. We can use the symbol [Ne]
to represent the configuration of the first 10 electrons and call it a neon core. Similarly 18
electrons arranged in the ground state of an argon atom (ls22s22p63s23p6) is written tAr]
and called an argon core. Krypton, xenon and radon cores can also be used. In practice, we
select the noble gas that most nearly precedes the element being considered. Therefore,
the electron configurations of the first five elements in the first (alkali metals) and eighth
(noble gas) groups are
As predicted, the electron configurations illustrate the electronic basis of the similarities
of chemical and physical properties observed in the groups of the periodic table, especially
when the nobel gas core is abbreviated. On the other hand, electron configurations tend to
hide information about the number of electrons in any one outer orbital. The 2p subshell
consists of three 2p orbitals: 2px, 2py, and 2pz. Therefore, the capacity of the subsheB is 6
electrons. In the case of elements with a partially filled orbital, carbon for example, a choice
arises about where to place the electrons. There are 2 electrons in the p subshell of a
carbon atom. Are both in the 2px orbital, or are they distributed so that the 2px and the 2py
orbitals each have one electron? An orbital diagram can simplify the choice. An orbital
diagram groups boxes that represent individual orbitals, to designate subshells.
is
2s
2p
Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms 133
An arrow pointing up 1" stands for an electron spinning in one direction, and an arrow
pointing down 4, stands for an electron spinning in the opposite direction. Electrons are
placed into orbitals according to Hund’s rule, which states that electrons entering a subshell
containing more than one orbital will have the most stable arrangement when the electrons
occupy the orbitals singly, rather than in pairs. Thus carbon has one electron in the 2px and
one in the 2py, rather than two e~ectrons in the 2px.
C
ls
2s
2p
is
2s
2p
Similary, Hund’s rule predicts that nitrogen atoms have the electrons in the 2p subshell
distributed with one each in the 2px, 2py, and 2pz. The orbital diagram indicates the number
of unpaired e~ectrons in an atom. The presence, or absence, of unpaired e~ectrons is
indicated experimentally by the behavior of an element when placed in a magnetic field.
Paramagnetic elements are attracted to a magnetic field because the atoms of
paramagnetic substances contain unpaired electrons. Diamagnetic elements are repulsed
by a magnetic field because the atoms of diamagnetic substances contain only paired
electrons.
Recapping the rules for writing electron configurations 1. Each shell (principal level) contains n subshells and a maximum total of 2n2
electrons
2. Each subshell contains 2~+1 orbitals
a. Electrons fill degenerate (equal energy) orbitals 1 at a time
3. Each orbital can hold up to 2 electrons.
4. Pairs of electrons in same orbital have opposite spins
5. The symbol of the preceding noble gas can be used to abbreviate the electron
configuration of the core electrons.
In most cases, you should be able to write the electron configuration of any
Examples
element on the periodic table. You will probably need guidance from Figure 7.24 7.9-7.11
of the text for transition metals, lanthanides and actinides, which exhibit nonsequential ordering of sublevels.
Exercises
7-18 - 7-21
Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms 135
GLOSSARY LIST
photon
wave-particle
duality
emission spectrum
quantum
electromagnetic
radiation
frequency
wavelength
amplitude
uncertainty
principle
wavefunction
electron cloud
electron density
atomic orbital
photoelectric effect
binding energy
quantum number (QN)
principal QN
angular momentum QN
magnetic QN
spin QN
ground state
excited state
electron configuration
Hund’s rule
Pauli exclusion principle
paramagnetic
diagmagnetic
EQUATIONS
Algebraic Equation
C=/~V
E=hv
R1
AEatom =-RH n2 ~ii2"
h
h
AxAp >-4~
English Translation
The wavelength of electromagnetic
radiation is inversely proportional to its
frequency.
138 Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms
WORKED EXAMPLES
EXAMPLE 7.1 Wavelength and Frequency
Domestic microwave ovens generate microwaves with a frequency of 2.450 GHz. What is
the wavelength of this microwave radiation?
¯ Solution
The equation relating the wavelength to the frequency is
C= Xv
where c is the speed of light.
Rearranging and substituting, we get:
c
v
3.0x103 m/s 1GHz
2.450 GHz 109/s
= 0,122 m
EXAMPLE 7.2 Planck’s Equation
The orange light given off by a sodium vapor lamp has a wavelength of 589 rim. What is the
energy of a single photon of this radiation?
Solution
The energy of a quantum is proportional to its frequency, Since wavelength is given here,
then substitute c/Z into Planck’s equation for v.
Ephoton = by -
ho
Substitute values for Planck’s constant and the speed of light into the equation, The units
will not cancel unless the wavelength is converted from nanometers into meters.
Ephoton = (6.63 x 10,34 J
s)(3.0 x 103 m/s) = 3.38 x 10-’m J
(589 x 10-em)
¯ Comment
We can compare this energy to that of a mole of substance. The energy of a mole of
)borons is the product of Ephoton x NA, where NA iS Avogadro’s number.
E = (3,38 x 10-!9 J)(6.02 x 1023/mol)
: 203,000 J/mo! = 203 kJ/mol
Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms 139
EXAMPLE 7.3 The Hydrogen Atom
a. What amount of energy, in joules, is lost by a hydrogen atom when an electron transition
from n = 3 to n = 2 occurs in the atom?
b. What is the wavelength of the light emitted by the transition described in part a?
¯ Solution for a
The energy of the atom is quantized and depends on the orbit of the electron. Each orbit is
assigned a principal quantum number n:
For this transition ni = 3 and nf = 2:
AE =Ef-Ei =E2-E3 = ~- - ~Substituting for RH gives:
AE = E2-E3 = "-218x10 18 J4 - (-218~10-t8 J)
AE =-0.545 x 10-18 J + 0.242 x 10-18 J
AE = -0.303 x 10 18 j = -3.03 x 10-19 J
Solution for b
The energy lost by the atom appears as a photon of radiation with its respective frequency
and wavelength. Since the energy of the photon is positive, we will drop the negative sign
from the calculation of the wavelength.
AEatom = Ephoton -
hc
v
hc
hc
AEatom
3.03x 10 19j
(6.63 x 10 34 j. s)(3.00 x 108 m/s)
3.03x10
~=656x10-gm =656nm
EXAMPLE 7.4 De Broglie Wavelength
When an atom of Th-232 undergoes radioactive decay, an alpha particle which has a mass
of 4.0 amu is ejected from the Th nucleus with a velocity of !.4 x 107 m/s. What is the de
Broglie wavelength of the alpha particle?
140 Chemistry, Ch. 7." Quantum Theory and the Electronic Structure of Atoms
o Solution
The de Broglie wavelength depends on the mass and velocity of the particle:
h
mu
Because Planck’s constant has units of J.s, and 1 J = 1 kg’m2/s2, the mass of the alpha
particle should be expressed in kg. Since 1 mole of alpha particles has a mass of 4.0 g, then
the mass of one particle is:
?kg
4.00× 10.3 kg/mol
= 6.64 x lO-27 kg/particte
particle 6.022 x 1023 particles/tool
The wavelength of this alpha particle is:
mu
(6.64 x 10_27 kg)(1.4 x 107 m/s)
Notice that all the units cancel except meters. The wavelength is:
~.= 7,1 x 10-15 m
¯ Comment
The wavelength is smaller than the diameter of the thorium nucleus, about 2 × 10-~4 m.
EXAMPLE 7.5 Quantum Numbers
If the principal quantum number of an electron is n = 2, what are allowed values for
Its ~ quantum number?
a.
Its m~ quantum number?
b.
c.
Its ms quantum number?
- Solution
a. Recall that the angular momentum quantum number ~ has values that depend on the
value of the principal quantum number n. ~ = 0, 1, 2, on up to the highest value (n - 1).
When n = 2, then ~ = 0, 1.
b. The magnetic quantum number m~ depends on the value of ~ where m~ = -4, -~ +1 .....
~ + 1, ~. There are two ~ values andso two sets of m~ values. When ~ = 1, then
=
me -1, 0, 1 ; and when [ = 0, then me = 0.
The ms quantum number for a single electron can be either +1/2 or -1/2.
EXAMPLE 7.6 Quantum Numbers and Orbitals
List all the possible types of orbitals associated with the principal energy level n = 5.
Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms 141
¯ Solution
The type of orbital is given b~ the angular momentum quantum number. When n = 5;
[ = 0, 1, 2, 3, and 4. These correspond to subshells consisting of s, p, d, and f orbitals.
EXAMPLE 7.7 Quantum Numbers
For the following sets of quantum numbers for electrons, indicate which quantum numbers
-- n, [, me -- could not occur and state why.
a. 3, 2, 2
b. 2, 2, 2
c. 2, 0,-1
Solution
a. When n = 3, then ~ = 0, 1, 2. When ~ = 2; then me =-2,-1, 0, 1, 2. Set (a) can occur.
b. When n = 2, then ~ = 0, 1. The set in (b) cannot occur because ~ # 2 when n = 2. This
means that the n = 2 principal level cannot have d orbitals.
c. When n = 2, ~ = 0, 1. When ~ = 0, me = 0. The set in (c) cannot occur because me # -1
when ~ = 0.
EXAMPLE 7.8 Quantum Numbers and Orbitals
What values can me take for
a. a 3d orbital?
b. a 2s orbital?
¯ Solution
The values of me depend only on [. First, convert each orbital designation to the
corresponding value of [, then list allowed values for me.
For a d orbital [ = 2; therefore, possible me values are -2, -1, O, 1, and 2.
a.
b.
For an s orbital ~ = O; therefore, me = O.
EXAMPLE 7.9 Electron Configurations
Which of the following electron configurations would correspond to ground states and which
to excited states?
a. 1s22s22p1
b. 1s22p1 c. ls22s22p13s~
o Solution
a. In this configuration electrons occupy the lowest possible energy states. It corresponds
to a ground state.
b. In this configuration electrons do not occupy the lowest possible energy states. The 2s
orbital which lies lower than the 2p is vacant, and the last electron is in the 2p orbital.
This is an excited state.
c. In this case the last electron is in the 3s orbital while the lower energy 2p subshell is not
completely filled. This is an excited state.
142 Chemistry, Ch. 7: Quantum Theory and the Electronic Structure of Atoms
-~XAMPLE 7.10 Electron Configurations
Write the electron configuration for a potassium atom.
o Solution
~otassium has 19 electrons. The first 10 of these will occupy the same orbitals as neon
which is given above: 1s22s22p6. .
This leaves 9 electrons to account for. Keeping in mind the order of increasing orbital
energies, the next 2 electrons fill the 3s orbital. Then 6 electrons can be placed into the 3p
subshell. This leaves 1 electron. According to the order of orbital energies, the 3d
does not fill next. Rather, the 4s orbital is lower in energy than the 3d. The last electron in
potassium enters the 4s orbital. The electron configuration of potassium is:
K
1s22s22p63s23p64s!
or in terms of the argon core abbreviation:
K
[Ar]4s~
EXAMPLE 7,11 Orbital Diagrams
a. Write the electron configuration for arsenic.
b. Draw its orbital diagram.
c. Are As atoms diamagnetic or paramagnetic?
Solution
From the atomic number of As we see there are 33 electrons per arsenic atom. From
Figure 7.23 in the text, the order of filling orbitals is ls, 2s, 2p, 3s, 3p, 4s, etc. Placing
electrons in the lowest energy orbitals until they are filled, the first 18 electrons are
arranged as ls22s22p63s23p6, corresponding to an Ar core. The next two enter the 4s,
and the next ten enter the 3d. This leaves 3 electrons for the 4p subshell. The electron
configuration of As is:
AS [Ar]4s23dl°4p3
b. All of the orbitals are filled except for the 4p orbitals. The electrons must be placed into
the 4p orbitals according to Hund’s rule. The diagram for the outer orbitals is!
4s
3d
4p
c. Arsenic atoms are paramagnetic because they contain 3 unpaired electrons.
J