2
1
ChemActivity
The Nuclear Atom
(What Is an Atom?)
Model: Schematic Diagrams for Various Atoms.
•
electron (—)
o proton (+)
1 amu = 1.6606 x 10
-24
g
O neutron (no charge)
The nucleus of an atom contains the protons and the neutrons.
Hydrogen
1
Hydrogen
2
H
Hydrogen ion
1 —
H
H
•
•
•
o •
oo
2.0140 amu
1.0078 amu
Carbon
1.0083 amu
Carbon
Carbon ion
13 C
12 C
•
•
•
•
6 protons
6 neutrons
exactly 12 amu
6 protons
7 neutrons
13.0034 amu
Oxygen ion
•
6 protons
7 neutrons
13.0039 amu
Sodium ion
23 Na+
16 o 2—
•
•
•
•
•
•
•
•
8 protons
8 neutrons
15.9960 amu
1 H and 2H are isotopes of hydrogen.
11 protons
12 neutrons
22.9893 amu
12C and 13C are isotopes of carbon.
ChemActivity 1
The Nuclear Atom
3
Critical Thinking Questions
I.
How many protons are found in 12C? 13C? 13C- ?
6, 6, 6
2. How many neutrons are found in 12C? 13C? 13C- ?
6, 7, 7
3. How many electrons are found in 12C? 13C? 13C- ?
6, 6, 7
4. Based on your answers to CTQs 1-3, what do all carbon atoms (and ions) have in
common?
6 protons
5. Based on the model, what do all hydrogen atoms (and ions) have in common?
1 proton
6. Based on your answers to CTQs 4 and 5, what is the significance of the atomic
number, Z, above each atomic symbol in the periodic table?
The number of protons
7. Based on your answer to CTQ 6, what do all nickel (Ni) atoms have in common?
28 protons
8. In terms of the numbers of protons, neutrons and electrons:
a)
Why does the notation 13C- have a negative sign in the upper right hand
corner?
It is an ion with a negative 1 charge
b)
What feature distinguishes a neutral atom from an ion?
Neutral atoms have no charge
c)
Provide an expression for calculating the charge on an ion.
protons - electrons
4
ChemActivity 1
The Nuclear Atom
9. Determine the number of protons, neutrons, and electrons in one 1 H+ ion. Explain
how you found your answer.
1 protons, 0 neutrons, 0 electrons
The atomic number of hydrogen is 1 but it has not neutrons
because its atomic mass number is also 1. 1-0=1 meaning
there are no electrons.
10. What structural feature is different in isotopes of a particular element?
different number of neutrons
11. How is the mass number, A, (left-hand superscript next to the atomic symbol as
shown in the Model) determined (from the structure of the atom)?
it is the number of protons plus neutrons
12.
Show that the mass number and charge given for 16 - 2- and 23N
Model 1.
are correct in
8 protons +8 neutrons =16 is the mass number shown, 8 protons -10 electrons = -2
11 protons + 12 neutrons = 23, 11 protons - 10 electrons = +1
13.
Based on the information in Model 1, where is most of the mass of an atom, within
the nucleus or outside of the nucleus? Explain your reasoning using grammatically
correct English sentences.
The most mass is in the nucleus because electron do not
play a role int he atomic weight or mass number
because their mass is insignificant in comparison to
protons and neutrons.
ChemActivity 1
The Nuclear Atom
5
Exercises
1. Complete the following table.
Isotope
Atomic
Number
Z
31p
15
Mass
Number
A
Number of
Electrons
31
15
18
8
19
39
18
28
58
26
8
180
39K+
58Ni2+
2. What is the mass (in grams) of a) one 1 H atom? b) one 12C atom?
a)1.6606 x 10^-24g
b)1.9927 x 10^-23g
3. What is the mass (in grams) of 4.35 x 106 atoms of 12C?
8.668 x 10^-13 g
4. What is the mass (in grams) of 6.022 x 1023 atoms of 12C?
12.000 g
5. What is the mass (in grams) of one molecule of methane which has one 12C atom
and four 1 H atoms, 12C1 H4?
2.657 x 10^-23g
6. a) Define mass number. b) Define atomic number.
a)protons+neutrons b)# of protons
7. Indicate whether the following statement is true or false and explain your reasoning.
An 180 atom contains the same number of protons, neutrons, and electrons.
False
8.
8-protons,10-neutrons,8-electrons
How many electrons, protons, and neutrons are found in each of the following?
24mg
23Na+
35C1
e-12
p-12
n-12
e-10
p-11
n-12
e-17
p-17
n-18
35C1-
e-18
p-17
n-18
56Fe3+
15N
e-23
p-26
n-30
e-7
p-7
n-8
1602-
27M3+
e-10
p-8
n-8
e-10
p-13
n-14
6
ChemActivity 1
The Nuclear Atom
9. Complete the following table.
Isotope
Atomic
Number
Z
27
Mass
Number
A
59
14N
7
14
7Li
3
7
3
6Li
3
6
3
30
58
28
9
19
10
59Co^24
58Zn2+
I 9F-
Number of
Electrons
25
7
10. Using grammatically correct English sentences, describe what the isotopes of an
element have in common and how they are different.
Common=same # of protons Difference= # of neutrons
Problems
1. Estimate the mass of one 14C atom (in amu) as precisely as you can (from the data
in the model). Explain your reasoning.
2. Use the data in Model 1 to estimate the values (in amu) of a) the mass of an
electron, b) the mass of a proton, and c) the mass of a neutron.
3. The mass values calculated in Problem 2 are only approximate because when atoms
(up through iron) are made (mainly in stars) from protons, neutrons, and electrons,
energy is released. Einstein's equation E = mc2 enables us to relate the energy
released to the mass loss in the formation of atoms. Use the known values for the
mass of a proton, 1.0073 amu, the mass of a neutron, 1.0087, and the mass of an
electron, 5.486 x 10-4 amu, to show that the mass of a 12C atom is less than the
sum of the masses of the constituent particles.
8
ChemActivity
3
Coulombic Potential Energy
(What Is Attractive about Chemistry?)
Model 1: Two Charged Particles Separated by a Distance "d".
• 1
0. •
particle 1
particle 2
charge on particle 1 = q1
charge on particle 2 = q2
v - 4(12
According to Coulomb, the potential energy (V) of two stationary charged particles is
given by the equation above, where qi and q2 are the charges on the particles (for
example: -1 for an electron), d is the separation of the particles (in pm), and k is a
positive-valued proportionality constant.
1 pm = 10-12 m
Critical Thinking Questions
I. Assuming that qi and q2 remain constant, what happens to the magnitude of V if the
separation, d, is increased?
The magnitude of V decreases
2. If the two particles are separated by an infinite distance (that is, d = Go), what is the
value of V?
V=0
3. If d is finite, and the particles have the same charge (that is, qi = q2), is V> 0 or is
V < 0? Explain your answer.
k and d must be positive. q1q2 must be
positive.Therefore, Vmust be positive. That is, V> 0
4. If q for an electron is -1,
q= +1 for a proton
a) what is q for a proton?
b) what is q for a neutron? q= 0 for a neutron
c) what is q for the nucleus of a C atom? q= +6 for the nucleus of a carbon atom
ChemActivity 3
Coulombic Potential Energy
9
5. Recall that a 1 H atom consists of a proton as the nucleus and an electron outside of
the nucleus. Is the potential energy, V. of a hydrogen atom a positive or negative
number? Explain your answer.
V is a negative number because k(1)(–1)/d is negative
Model 2: Ionization Energy.
The ionization energy (1E) is the amount of energy needed to remove an electron
from an atom and move it infinitely far away. Ionization energies are commonly
measured in joules, J.
Figure 1.
Ionization of a hypothetical atom L with one proton and one
stationary electron.
Adding 0.231 x 10-18 J to Atom L results
in a bare proton and a free electron.
IE = 0.231 x 10-18 J
Atom L + 0.231 x 10-18 J
Figure 2.
Ionization energies of two hypothetical atoms, each with one
proton and one stationary electron separated by distance "d".
d = 500 pm
d= 200 pm
IE = 0.462 x 10 -18 J
IE= 1.16 x 10-18J
10
ChemActivity 3
Coulombic Potential Energy
Table 1.
Ionization energies of several hypothetical atoms,
each with one proton and one stationary electron
separated by distance "d".
Hypothetical
IE
V
(10-18
Atom
(10-18 J)
(pm)
co
A
0
5000.
0.0462
1000.
0.231
500.0
0.462
200.0
1.16
100.0
2.31
Critical Thinking Questions
6. Do you expect the potential energy, V, of the hypothetical atoms in Table 1 to be
positive or negative numbers? Explain your reasoning.
V is negative because the electron is negative and the proton is positive
7. Without using a calculator, predict what trend (if any) you expect for the values of
V for these hypothetical atoms.
I would expect V to be become more
negative as d becomes smaller
8. Calculate the potential energies of the hypothetical atoms to complete Table 1. Use
the value k= 2.31 x 10-16 J•pm.
V(10–18J) = 0, –.0462, –0.231, –0.462, –1.16, –2.31
9. What is the relationship between IE and V for these hypothetical atoms?
V= –IE
10. Which of the following systems will have the larger ionization energy? Explain
your reasoning.
a) an electron at a distance of 500 pm from a nucleus with charge +2
b) an electron at a distance of 700 pm from a nucleus with charge +2
a) The electron that is closer to the nucleus would have the larger
ionization energy because it is at a lower (more negative)
potential energy according to Coulomb’s potential energy equation
ChemActivity 3
11.
Coulombic Potential Energy
11
Which of the following systems will have the larger ionization energy? Explain
your reasoning.
a)
b)
an electron at a distance d1 from a nucleus with charge +2
an electron at a distance d1 from a nucleus with charge +1
a) The electron that is at d1 from the +2 nucleus
would have the larger ionization energy because
it is at a lower (more negative) potential energy
according to Coulomb’s potential energy equation
12. How many times larger is the larger of the two ionization energies from CTQ 11?
Show your work.
The ionization energy is larger by a factor of 2
13. Consider a hydrogen atom and a helium ion, Het Which of these do you expect to
have the larger ionization energy? Explain your reasoning, including any
assumptions you make.
He+ would have a larger ionization energy than H because q= +2
for He and it would have a lower (more negative) potential
energy according to Coulomb’s potential energy equation
12
ChemActivity 3
Coulombic Potential Energy
Exercises
1. For a hypothetical atom (as in Table 1) with V = -5.47 x 10-18 J, what would the IE
be?
IE= 5.47 x 10^-18 J
2. Which of the following systems will have the larger ionization energy? Show your
work.
a is larger because
a) an electron at a distance d1 from a nucleus with charge +2
a. V = k(+2)(-1)/d
b) an electron at a distance 2d1 from a nucleus with charge +1
b. V = k(+1)(-1)/2d
3. Which of the following systems has the larger ionization energy?
a is larger because
a) an electron at a distance 5d1 from a nucleus with a charge of +6
a. V = k(+6)(-1)/5d
b) an electron at a distance 6d1 from a nucleus with a charge of +7
b. V = k(+7)(-1)/6d
Problems
I. According to the Coulombic Potential Energy equation, if a particle with a charge
of -1 is extremely close to a particle with a charge of +2, the potential energy is: a)
large and positive b) large and negative c) small and negative d) small and
positive
B
2. Two electrons and one helium nucleus are arranged in a straight line as shown
below. The electron on the left is 300 nm from the nucleus; the electron on the
right is 400 nm from the nucleus. Write the three Coulombic Potential Energy
terms for this arrangement of charges.
electron
300 pm +2
V = k(+2)(-1)/300
electron
nucleus
400 pm
-1
V = k(+2)(-1)/400
V = k(-1)(-1)/700
14
ChemActivity
4
The Shell Model (I)
(How Are Electrons Arranged?)
Electrons in atoms are attracted to the nucleus by a Coulombic force. Thus, energy
must be supplied (by some means) if the electron is to be pulled away from the nucleus,
thereby creating a positively charged species, or cation, and a free electron. For real
atoms, the ionization energy (IE) of an element is the minimum energy required to
remove an electron from a gaseous atom of that element.
Ionization energies are usually obtained experimentally. One method of measuring
ionization energies is the electron impact method. Atoms are bombarded with fastmoving electrons. If these electrons have sufficient energy, they will, on colliding with
an atom, eject one of the atom's electrons. The ionization energy described above (often
called the first ionization energy) corresponds to the smallest amount of energy that a
bombarding electron needs to be able to knock off one of the atom's electrons.
Model 1: First Ionization Energy (1E1).
M(g)
(g) +
For a H atom, 1E = 2.178 x 10-18 J.
The first ionization energy, IE1, for a single atom is a very small number of joules.
For reasons of convenience, chemists have chosen to report the ionization energies of
elements in terms of the minimum energy necessary to remove a single electron from
each of a mole of atoms of a given element. This results in ionization energies for the
elements that are in the range of MJ/mole. (Note that 1 MJ = 106 J.)
Critical Thinking Questions
. How much total energy would it take to remove the electrons from a mole of H
atoms? Write this energy in MJ/mole.
1.31 MJ/mole
2. For atoms with many electrons, not all electrons are at the same distance from the
nucleus. In this case, which electron would have the lowest ionization energy: the
electron that is closest to the nucleus or the electron that is farthest from the
nucleus? Explain.
The electron that isfarthest from the nucleus
will have the least negative potential energy
(d is larger) and the lowest ionization energy
ChemActivity 4
The Shell Model (I)
15
3. Predict the relationship between IE1 and atomic number by making a rough graph
of IE1 vs. atomic number. DO NOT PROCEED TO THE NEXT PAGE UNTIL
YOU HAVE COMPLETED THIS GRAPH.
IE1
(N4J/nlole)
Atomic Number
16
ChemActivity 4
The Shell Model (I)
Information
Based on our previous examination of ionization energies, it is expected that the
ionization energy of an atom would increase as the nuclear charge, Z, increases. In
addition, the ionization energy of an atom should decrease if the electron being removed
is moved farther from the nucleus (that is, if d increases).
Table 1 below presents the experimentally measured ionization energies of the first
20 elements. We will examine these results and attempt to propose a model for the
structure of atoms based on these data.
Table 1.
1
2
3
4
5
6
7
8
9
10
First Ionization energies of the first 20 elements.
Z
IE1
IE1
(MJ/mole)
(MJ/mole)
11 Na
0.50
H
1.31
He
2.37
12 Mg
0.74
Li
0.52
13 Al
0.58
Be
0.90
14 Si
0.79
B
0.80
15 P
1.01
16 S
1.00
C
1.09
N
1.40
17 Cl
1.25
18 Ar
1.52
0
1.31
F
1.68
19 K
0.42
20 Ca
Ne
2.08
0.59
Critical Thinking Questions
4. Compare your answer to CTQ 3 to the data in Table 1.
similarities and differences.
Comment on any
The first table in increasing as my graph is because
the atomic number is higher nuclear charge while the
second table differs because of the electrons being
farther away from the nucleus
5. Using grammatically correct English sentences:
a) provide a possible explanation for why IE1 for He is greater than IE1 for H.
a) The IE1for He is greater than the IE1for H
because the nuclear charge on a He atom is
+2 whereas the nuclear charge on H is +1.
b) provide a possible explanation for why IE1 for Li is less than IE1 for He.
b) The IE1for Li is less than the IE1for He because at least
one of the electrons of Li must be farther away from the nucleus
than any electron of He.Otherwise, the +3 nuclear charge of
Li would hold the electron more tightly.
ChemActivity 4
The Shell Model (I)
17
Model 2: Simple Model Diagrams for Hydrogen and Helium
Atoms.
One simple model of the hydrogen atom pictures the H atom as a nucleus of charge
+I surrounded by an electron at some distance, as shown in Figure 1.
Figure 1.
Model diagram of a hydrogen atom.
electron \
the electron "sees" a
+1 charge at the nucleus
Figure 2.
Model diagram of a helium atom.
each electron "sees" a
+2 charge at the nucleus
Examining the data in Table 1, we note that the ionization energy of He (Z=2) is
larger than that of H (Z=I) by approximately a factor of 2. This is consistent with the
two electrons in the He atom at a distance (from the nucleus) approximately the same as
that in H.
Critical Thinking Question
6. The value of the ionization energy of He given in Table 1 is described as being
consistent with two electrons in a "shell" approximately the same distance from the
nucleus as the one electron in H. Use the Coulombic Potential Energy equation,
kqq
V —
2 to explain how this conclusion can be reached.
Hint: recall the
relationship between V and IEI.
Each electron is held by a +2 charge, rather than a +1 as in H.
Therefore, if the electrons is He and H are at the same distancethe
Coulombic Potential Energy for He ought twice the Coulombic Potential
for He and IE1for He ought to be about 2 x IE1for H
18
ChemActivity 4
The Shell Model (I)
Information
Because the He nucleus has a charge of +2, we would expect that the ionization
energy to remove an electron from (approximately) the same distance as in a H atom
would be (approximately) twice that of the H atom. That is what we observe. We can
say that there are two electrons in a shell around the He nucleus. Although we will
present figures in which the shells appear to be circular (mostly because it is difficult to
present three-dimensional representations on paper), we recognize that the model we
develop is qualitatively consistent with spherical shells. Thus, within our Shell Model,
He consists of a nucleus surrounded by 2 electrons in a single shell.
Critical Thinking Questions
7. Recall that the IE of H is 1.31 MJ/mole. If all three electrons in Li were in the first
shell at a distance equal to that of hydrogen, which of the following values would
be the better estimate of the lEi of Li: 3.6 MJ/mole or 0.6 MJ/mole? Explain.
If the 3rd electron was at the same distance as H, the
IE1would be about 3 xIE1for H—3.93 MJ/mole. However, it
would be a bit less because of the repulsion between
the electrons; the best answer is 3.6 MJ/mole
8. A student proposes a model for the Li atom in which all three electrons are in the
first shell at a distance approximately the same as in H. Why is this model not
consistent with the 1E1 for Li in Table 1?
For this model the IE1of Li would be about 3.93 MJ/mole
(probably a bit less due to the repulsion between the
electrons—see the previous CTQ). The IE1 of Li is 0.52
MJ/mole—much smaller than 3.93MJ/mole (see the
previous CTQ). This low value is inconsistent with the
least tightly held electron being this close to the nucleus.
9. Another student proposes a model for the Li atom in which two electrons are in the
first shell (as in He) and the third electron is much farther from the Li nucleus.
Explain why this model is consistent with the 'El for Li in Table 1.
If the 3rd electron is farther away from the nucleus
than the electron in H the IE1would be much lower
that the IE1for H.Because the IE1 of Li is 0.52 MJ/
mole and the IE1 of H is 0.52 MJ/mole, this model
is consistent with the experimental data
ChemActivity 4
The Shell Model (I)
19
Model 3: The Shell Model for Lithium.
For Li, there is a change in the trend of the ionization energy. The ionization energy
of a Li atom is less than that of He. In fact, it is significantly smaller than that of the H
atom! This is not consistent with a model of placing a third electron in the first shell, for
doing so would result in an ionization energy which is larger than that of He. In order for
Li to have a lower ionization energy than H, either the nuclear charge Z must be lower
than that of H, or the distance of the easiest-to-remove electron from the nucleus must be
greater than in H (and He), or both. We know that the nuclear charge is not lower than
that of H; thus, the electron being removed must be farther from the nucleus than the first
shell. Although the data we have does not require us to choose the following model, let
us assume that the structure of Li involves two electrons in a first shell (as in He) with the
third electron placed in a second shell, with a significantly larger radius, as shown in
Figure 3.
Figure 3.
Diagram of a lithium atom using the shell model.
Critical Thinking Question
10. Is the amount of energy required to remove one of the electrons from the first shell
of Li greater than, less than, or equal to the IE1 for Li? Explain your reasoning.
The electrons in the first shell of Li are
closer to the nucleus and should be harder
to ionize (have a greater ionization energy)
than the electron in the second shell.
20
ChemActivity 4
The Shell Model (I)
Exercises
1. A scientist proposes a model for the helium atom in which both electrons are in a
"shell" which is half the distance from the nucleus as the electron in a hydrogen
atom. Is this model consistent with the data in Table 1? Explain your reasoning.
(Hint: according to the Coulombic Potential Energy equation, how much more
strongly does a nuclear charge of +2, as in He, hold an electron than a nuclear
charge of +1, as in H? According to the Coulombic Potential Energy equation, how
much more strongly does a nuclear charge hold an electron if it is at d/2, rather than
No, the IE in the case above would be 4x greater
d?)
as the e- would be twice as close to the nucleus
2. Propose an alternative model for the lithium atom which is consistent with the data
in Table 1.
v= (+1)(-1)/3d
+3
Problem
1. a) Write the three Coulombic Potential Energy terms for the helium atom model in
Figure 2. Assume that the distance between each electron and the nucleus is d and
that the distance between the two electrons is 2d.
The electron that is farther from the nucleus.
b) Based on your answer to part a) explain why the IE of He is slightly less than
twice the IE of H even though both atoms are about the same size.
It has the least negative potential energy (because
potential energy becomes more negative as the electron
gets closer); therefore, that electron has the least IE.
22
ChemActivity
5
The Shell Model (II)
Model 1: Valence Electrons, Inner-Shell Electrons, and Core
Charge.
The electrons in the outermost shell of an atom are referred to as valence electrons.
Electrons in shells closer to the nucleus are called inner-shell electrons. Thus, Li has one
valence electron and two inner-shell electrons. H has one valence electron and no innershell electrons.
The nucleus plus the inner shells of electrons constitute the core of the atom, and the
net overall charge on the core is called the core charge. We can represent the Li atom in
terms of core charge as shown in Figure 1.
Figure 1.
Diagram of a lithium atom using the shell model (a) and the
core charge concept (b).
(a)
inner-shell or
core electron
valence
electron
core
charge
(b)
valence
electron
ChemActivity 5
The Shell Model (II)
23
Critical Thinking Questions
1. How many electrons are in the valence shell of a) H? b) Li? C) He?
a)H, one electron
b) Li,,one electron c) He, two electrons
2. How many inner-shell electrons are there in a) H? b) Li? C) He?
a) H, zero b) Li, two c)He, zero
3. What is the core charge of Li?
The core charge of Li is +1
Model 2: Core Charge and Electron-Electron Repulsion.
Notice that within the model of the Li atom, shown in Figure 1, the valence electron
is farther from the nucleus than the two inner-shell electrons. Although we have ignored
it up to this point, we should remember that all of the electrons repel each other because
they are negatively charged. Of particular interest is the repulsion of the valence electron
by the two inner-shell electrons. This dramatically decreases the overall force of
attraction pulling the valence electron toward the nucleus.
Critical Thinking Question
4. Two possible models for arrangement of electrons in Li are shown below:
electron "a"
electron "b"
ra = rb
Explain why the IE1 of electron "b" would be less than the !El of electron "a".
Electron “b” experiences more electron-electron repulsion than electron “a”
because electron “a” is farther from the other electrons than electron “b”.
Therefore the IE1 of electron “b” would be less than the IE1 of electron “a”.
24
ChemActivity 5
The Shell Model (II)
Model 3: The Beryllium Atom.
The next element, Be, has an ionization energy which is larger than that for Li. This
is consistent with the fourth electron in Be being added to the second shell. Thus, Be has
2 valence electrons and a core charge of +2. Two representations of the Be atom are
given in Figure 2.
Figure 2.
Diagram of a Be atom using the shell model (a) and the core
charge concept (b).
(a)
(b)
the valence electron "sees" a
core charge of +2
Critical Thinking Questions
5. a) Why is the nuclear charge of Be "+4"?
Be has 4 protons in its nucleus
b) How many inner-shell electrons does Be have?
2
c) How many valence electrons does Be have?
2
d) Show how the core charge for Be was calculated.
4-2=2
e) What is the relationship between the number of valence electrons and the core
charge of a neutral atom?
The core charge is equal to the number of valence electrons for a neutral atom
6. Assuming that the valence shells of Li and Be are at approximately the same
distance from their nuclei, explain how the core charges of Li and Be are consistent
with the IE1 values for Li (0.52 MJ/mole) and Be (0.90 MJ/mole).
Be has a higher core charge(+2) than Li (+1) and a higher IE1 than Li
ChemActivity 5
The Shell Model (II)
25
Information
As described above, the outer-shell valence electrons experience the charge of the
core rather than the full charge of the nucleus. The inner electrons that surround the
nucleus are said to shield the nucleus. In fact, because the valence electrons are all
negatively charged, they repel each other also. Thus the net resulting charge acting on a
valence electron to attract it toward the nucleus differs from the core charge. This overall
resulting charge acting on a valence shell electron is known as the effective nuclear
charge, and it is generally less than the core charge. Since there is no simple way to
obtain values for the effective nuclear charge, we will use the core charge as a basis for
our qualitative explanations. It is only an approximation, but it is adequate for our
purposes.
Model 4: The Neon Atom.
Although there are some slight variations, in general there is an increase in ionization
energy as the atomic number further increases up to Z = 10 (Ne). This is qualitatively
consistent with an increase in core charge. (The slight variations will be addressed later.)
There is no large drop in ionization energy to a value less than that of H, as we observed
in going from He to Li, to indicate that a third shell is needed. This suggests that as we
move from Be up to Ne, the number of electrons in the second shell increases.
Figure 3.
Diagram of a Ne atom using the shell model (a) and the core
charge concept (b).
(a)
(b)
the valence electron "sees" a
core charge of +8
Ne has 8 electrons in the second (valence) shell, and 2 electrons in the inner (first) shell.
Notice that we can number the shells based on their distance from the nucleus. We can
let the number "n" represent the number of the shell an electron is in. Thus, Ne has 2
electrons in the n = 1 shell and 8 electrons in the n = 2 shell.
Critical Thinking Questions
7. Show how the core charge for Ne was calculated.
Ne: 10–2 = 8
26
ChemActivity 5
The Shell Model (II)
8. Make two diagrams, similar to Figures 3(a) and (b), for the nitrogen atom.
+5
+7
9.
a)
Make two diagrams, similar to Figures 3(a) and (b), for the sodium atom,
assuming that the 11th electron goes into the second shell.
+9
+11
b)
What is the core charge for the sodium atom in CTQ 9a?
+9
c)
The IE1 of Ne is 2.08 MJ/mole. Predict whether the IE1 for the Na atom in
CTQ 9a would be greater than, less than, or equal to 2.08 MJ/mole. Explain
your reasoning.
Because the core charge of Ne is +8 and the core charge of Na is
+9(and because the electrons are about the same distance from the
nuclei) the IE1for Na should be greater than 2.08 MJ/mole.
10.
a)
Make two diagrams, similar to Figures 3(a) and (b), for the sodium atom,
assuming that the 11th electron goes into a new, third shell.
+11
b)
What is the core charge for the sodium atom in CTQ 10a?
+1
c)
Predict whether the IE1 for the Na atom in CTQ 10a would be greater than,
less than, or equal to 2.08 MJ/mole. Explain your reasoning.
Because the core charge of Ne is +8 and the core charge of Na
is +1 (and because the outermost Na electron is farther from the
nucleus) the IE1for Na should be much less than 2.08 MJ/mole.
11. The experimental IE1 for Na is 0.50 MJ/mole. Use this datum to explain why the
model for Na suggested in CTQ 10 is a better model than the one suggested in CTQ
9.
The experimental IE1for Na is 0.50 MJ/mole. This is consistent with the model in CTQ 10
ChemActivity 5
The Shell Model (II)
27
Model 5: The Sodium Atom.
Diagram of a Na atom using the shell model (a) and the core
charge concept (b).
(a)
(b)
Critical Thinking Questions
12. How many electrons does Na have in shell n = 1? n = 2? n = 3?
2, 8, 1
13. How does the core charge for Na compare to the core charge for Li?
Both have a core charge of +1
14. Based on your answer to CTQ 13 and the ionization energy data, Table 1 of
ChemActivity 4: Shell Model (I), is the radius of the valence shell of Na larger,
smaller or the same as the radius of the valence shell of Li?
The radius of the valence shell of Na is larger than the
radius of the valence shell of Li because they both have a core
charge of +1 and Na has the lower IE1
15. Consider the models of Ne and Na shown in Models 4 and 5. Explain how the core
charges of Na and Ne are qualitatively consistent with the IE1 data in Table 1 of
ChemActivity 4: Shell Model (I).
Na has a core charge of +1 and Ne has a core charge of +8. Na should
have a much lower IE1. The is consistent with the experimental data
28
ChemActivity 5
The Shell Model (II)
Information
The 1E1 for Na is 0.50 MJ/mole, much less than the lE i for Ne. This decrease is
analogous to (and similar in magnitude to) that observed in going from He to Li. Note
that the ionization energy of Na is only 0.50 MJ/mole, even less (although only slightly
so) than that of Li. Analogous to the conclusions we reached concerning the structure of
the Li atom, these results suggest that the eleventh electron in Na should be placed in a
third shell (n = 3), at a slightly greater distance from the nucleus than the second shell is
for Li. Thus, it appears that the n = 2 shell can accommodate only eight electrons.
(Recall that the n = 1 shell holds only two.)
The pattern of ionization energies for the elements with Z = 11 to Z = 18 follows the
trend we previously identified for Z = 3 to Z = 10: a general increase (with slight
variations).
Critical Thinking Question
16. Use the core charge concept to propose an explanation for the increase of W I from
Na through Ar. Clearly state any assumptions that you make.
IE1 increases as we move from left to right from Na to Arbecause the
core charge increases for +1 to +8and the potential energy of the
electron becomes more negative according to the Coulombic potential
energy equation (the distance from the nucleus remaining fairly constant)
Information
As suggested by the data in Table 1 of ChemActivity 4: Shell Model (I), all of the
atoms in Group IA, the alkali metals, have a core charge of +1 and all of the atoms in
Group 7A, the halogens, have a core charge of +7. In fact, for Groups IA through 7A,
the atoms in each group all have the same number of valence electrons, and that number
is reflected by the group number. In all cases, the ionization energy decreases as we
move down the group. This pattern is also observed in Group 8A, the Noble (or Inert)
gases. However, not all of the atoms we have examined in Group 8A have eight valence
electrons (and a core charge of +8). Helium has only 2 electrons, a seeming violation of
the pattern we have uncovered. The resolution of this apparent inconsistency is that
although He has only 2 valence electrons, its valence shell is completelyfilled. The same
is true of Ne, although for Ne a filled valence shell has 8 electrons. Thus, we find that the
structure of the elements using this shell model is reflected in the placement of the
elements in the periodic table.
ChemActivity 5
The Shell Model (II)
29
Model 6: The Shell Model and Ionization Energies.
Table 1. Atomic Properties of Various Atoms.
Element
Valence Shell
Number of
Core Charge
(n)
Valence Electrons
H
1
1
+1
2
1
Li
+1
1
Na
3
+1
Rb
2
7
+7
F
+7
Cl
3
7
IE1
(MJ/mole)
1.31
0.52
0.50
0.40
1.68
1.25
Critical Thinking Questions
17. Locate H, Li, and Na on the periodic table.
a)
Describe any relationship between the core charge of these atoms, the
number of valence electrons, and their positions in the periodic table.
All three atoms have a core charge of +1 and all three atoms
are in the first column (labeled I)
b)
Describe any relationship between the valence shell of these atoms and their
positions in the periodic table.
The valence shell of H is 1 and it is found in the first row of the table. The
valence shell of Li is 2 and it is found in the second row. The valence shell
of Na is 3 and it is found in the third row.
c)
Based on its position in the periodic table, predict the valence shell, core
charge, and number of valence electrons for Rb and add these values to
Table 1. For Rb, the valence shell is 5, the core charge is
d)
Using the shell model and referring to the Coulombic Potential Energy
relationship (equation in Model I, CA3), explain clearly how the IE1 for Rb
is consistent with your answer to part c.
+1, and the number of valence electrons is 1.
18.
Rb has the lowest IE1of these four elements. This is consistent
with all four having one valence electron and a core
charge of +1, but the valence electron of Rb is farther from
the nucleus (higher numbered valence shell)
Construct a shell model diagram of F that is consistent with the information in
Table 1.
+9
+7
30
19.
ChemActivity 5
The Shell Model (II)
Locate F and Cl on the periodic table.
a)
Describe any relationship between the core charge of these atoms, the
number of valence electrons, and their position in the periodic table.
Both atoms have a core charge of +7 and 7 valence electrons, and both are found in the column labeled VII.
b)
Describe any relationship between the valence shell of these atoms and their
position in the periodic table.
The valence shell of F is 2 and it is found in
the second row. The valence shell of Cl is
3 and it is found in the third row
c)
Within our model and referring to the Coulombic Potential Energy
expression, explain why the IE1 of Cl is less than that of F.
The IE1of Cl is less than the IE1of F because
they both have a core charge of +7 but the
valence electrons of Cl are farther from the
nucleus than the valence electrons of F
20.
Based on its position in the periodic table, what is the valence shell and what is the
core charge for C? Explain your reasoning.
C is found in column IV, second row. Therefore, the core charge is
+4 and the four valence electrons are found in the second shell
21.
How does the core charge on the neutral atom change as we move from left to right
across a row (period) of the periodic table?
The core charge increases as we move from left to right across a period
22.
Within our model and referring to the Coulombic Potential Energy expression,
explain why the IE increases from left to right across a row of the periodic table.
IE1increases as we move from left to right across a
period because the core charge increases and the potential
energy of the electron becomes more negative according to
the Coulombic potential energy equation (the distance
from the nucleus remaining fairly constant)
ChemActivity 5
The Shell Model (II)
31
Exercises
1. How many valence electrons are there in: a) C? b) 0? c) N? d) Ne?
4, 6, 5, 10
2. What is the core charge for: a) C? b) 0? c) N? d) Ne?
+6, +6, 0, +1
3. Based on the information in Table 1 of ChemActivity 4: Shell Model (I), estimate
the ionization energy for Br. Explain your reasoning.
11.8138 eV the math
4. If a single electron is removed from a Li atom, the resulting Li+ cation has only two
electrons, both in the n = 1 shell. In this respect it is very similar to a He atom.
How would you expect the ionization energy of a Li+ cation to compare to that of a
He atom? Explain your reasoning.
If a single electron is removed from a Li atom, the resulting species is a Li+ cation, which has only two
electrons that are both in the n = 1 shell.
5. If a single electron is somehow added to a F atom, the resulting F+ anion has a total
of 8 valence electrons in the n = 2 shell. In this respect it is very similar to a Ne
atom. How would you expect the ionization energy of a F anion to compare to
that of a Ne atom? Explain your reasoning.
Between oxygen and fluorine the pairing up isn't a new factor, and the only difference in this case is the extra proton. So
relative to oxygen, the ionisation energy of fluorine is greater. And, similarly, the ionisation energy of neon is greater still
6. Predict the order of the ionization energies for the atoms Br, Kr, and Rb. Explain
your reasoning. Bromine has higher first ionization energy because it is more
electronegative and has 5 electrons in valence shell.
7. The radius of the outer shell in Li is larger than the radius of the inner shell. Which
electron is harder to remove the valence electron or one of the inner shell
electrons? Explain.
Inner shell electrons are closer to the nucleus and
closer to the protons, which pull the shell towards it.
Problems
1. Indicate whether each of the following statements is true or false and explain your
reasoning.
False bc it has a core charge of 35 which means it
a) The core charge of Br is +7. need more than 7 and the real charge is 28
True bc the first ionization energy varies in a predictable way across the periodic table.
b) Helium has the largest 1st ionization energy. The ionization energy decreases from top to bottom in groups, and increases from left to
right across a period. Thus, helium has the largest first ionization energy
2. Explain how the model of the structure of Be having the fourth electron in a third
shell, further from the nucleus than any of the three electrons in Li, is not consistent
with the experimentally obtained ionization energies.
As electrons get further from the nucleus less energy is required to remove the
electron from the atom;
As electrons are closer to the nucleus it requires more energy to remove the
electron;