Download Measurement of Ionization Energy

Topic 4.2 & 4.4 ATOMIC THEORY
SSC & HLS CHEMISTRY - ChemPhys Systems
Developing an Energy Level Model for Atoms Using Experimental Data
Measurement of Ionization Energy
E1 represents the energy required to remove the first electron from a gaseous atom, E 2 for the second and Em for
the mth electron. Measurement of Em involves transferring energy to the atom and detecting electrons when they
are dislodged. For example, atoms can be bombarded with projectiles of known energy and any electrons released
can be detected by their electrical conductivity.
The adjacent sequence of diagrams illustrates the
basic components required to measure ionization
energies. The projectile energy r
increased slowly until there is a jump in
conductivity. The energy of the projectiles that
causes the jump in conductivity is called the
ionization energy.
When the filament circuit is closed the battery B
F causes current to flow through the B, tungsten
filament F, heating it to red heat. Electrons are
vaporised from the red-hot tungsten.
Electrons coming out of the filament are
accelerated by the positively charged plate G.
The accelerated electrons act as projectiles. The
energy of the projectiles is determined by the
slide wire setting, V.
A sensitive current detector, microammeter A
with probes P and N completes the circuitry. The
device is enclosed in a glass envelope so air can
be removed and a test gas added. Suppose neon
is placed in the cell. In the region between G and
projectiles have sufficient energy, ionization of
the neon atom occurs. The dislodged electrons
are attracted to the positive electrode P and the
positive neon ions are attracted to the negative
electrode N. As some of these charges reach P
and N they cause current to flow through
ammeter A.
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The following graphs show the results of two experiments, the first using neon gas and the second using sodium
vapour. Sodium vapour was obtained by heating sodium metal at a temperature near 500 0C. The horizontal axis
shows the voltage, V as it was varied by moving the slide wire contact.
What values of V correspond to the first and second ionization energies of neon and sodium?
Neon V1
_____
Sodium V1
_____
V2
_____
V2
_____
Suggestions to Help Guide Your Search for an Energy Level Model for
Atoms
This activity is a dry lab. Your task is to develop a model from the provided data and write a report describing
what you did and what you developed. The data you will be using was measured about 30 years ago. The IB
Criteria that you will practise in this activity are “Planning (a) & (b), Data Analysis, Evaluation, Personal
Skills (a) & (b)”. Historically the energy level model was developed in 1913 from emission spectra by Niels
Bohr, 1885-1962. A treatment of his work is found in most introductory Chemistry or Physics texts. The
questions and information provided in this activity are here to help you develop an energy level model for atoms.
However, your report should not just be a series of answers to these questions. You should work with two or
three of your peers. Part of the evaluation of Personal Skills (b) will be based on your groups completion of the
“Group Evaluation Form”. Make sure you read over “Appendix A: Co-operative Learning” before you start
working in a group.
1. File IEII.XLS contains the ionization energies of the first 20 elements in eV as reported in the “Handbook of
Chemistry and Physics”. Before doing anything with the data convert the ionization energies to more familiar
units, kJ/mol.
2. What regularities can you see in the data?
3. If your first reaction on viewing the table was, “Yech, what a bunch of numbers!” it is understandable. A
mass of data like that is unmanageable. How might the data be reorganised to make any regularity more
obvious?
4. As a start, plot E1 versus Z on graph paper. Plot Z on the horizontal axis. NOTE: You may have done this in
a previous activity. If so, just examine your graph.
5. Describe the general shape of the graph.
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SSC & HLS CHEMISTRY - ChemPhys Systems
6. Compare the graph of E1 versus Z with the graph of “combining power” versus Z. How are the two graphs
similar? How do they differ?
7. Does the comparison support or reject the assumption that combining power is related to ionization energy?
Explain why you think so.
8. The fact that the period of repetition is the same is not proof that ionization energy is related to combining
power. However, it is a good indication that an energy description of the arrangement of electrons in an atom
might lead to an adequate model for combining power and hence chemical properties. To try to establish
further credibility we will first apply simple ideas of electrostatics to the nucleus-electron system and then
look at regularities in the ionization energies for a given atom.
Ionization Energy and Electrostatics
The electrons, which we are trying to remove, are attracted by the positive nucleus.
The nuclear charge, Z+, keeps the electrons from escaping. Assume that the attraction
is described by Coulomb'
9. What is Coulomb's Law? Write it as a mathematical equation. HINT: The
equation for Coulomb's Law has the same form as that describing the gravitational
force between two masses.
10. What variables will determine the magnitude of the attraction between the nucleus
and a given electron?
11. Thus, if Coulomb’s Law applies, the magnitude of the nuclear charge and the distance the electron is from the
nucleus will determine the attractive force. Now let us consider the fact that there is more than one electron
spinning around the nucleus. We assume that the Z electrons of an atom neutralise the Z+ charge on the
nucleus to make the atom neutral. Thus, how much of the nuclear charge will be neutralised by Z-1
electrons?
12. Thus, what is the NET nuclear charge that must be overcome to remove the first electron?
13. Substitute in the equation for Coulomb's Law to obtain an expression for the attractive force that must be
overcome to remove the first electron.
14. This expression is a mathematical model for the attractive force. On what assumptions is this model based?
15. What data is necessary before you can use the expression to determine the force attracting the first electron in
various atoms?
16. See “The Sargent-Welch Table of Periodic Properties of the Elements” for appropriate data. Determine the
trend in radius across a period, down a group. Predict the variation in the force of attraction for the first
electron across a period, down a group. Compare your predictions with the trends in the first ionization
energy across a period and down a group. How are they the same? How do they differ?
Trend in Radius
Predicted Trend in Force
Trend in ionization Energy
Across a period _____
Across a period _____
Across a period _____
Down a group _____
Down a group _____
Down a group _____
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17. Explain why you feel that the application of the principles of electrostatics adds or does not add credibility to
the assumption that combining power is related to the arrangement of electrons in an atom.
Successive Ionization Energies, Em
All neutral atoms, except hydrogen, have more than one electron. For multi-electron atoms, there are three
completely different electron arrangements possible. All electrons could have the same energy or they could all
have different energies. The third possibility is that some electrons have the same energy and that another group
of electrons have a different energy. Thomson suggested
“groups of electrons” were responsible for “the gradual change in properties of the elements as we travel
along the rows in the periodic table”.
18. Perhaps you can use ionization energies to see if he was right. Examine the successive ionization energies in
the file IEII.XLS. What evidence suggests that not all electrons in a given atom have the same energy?
19. What evidence suggests that there are groups of very similar electrons in a given atom? (NOTE: If you are
very perceptive and are able to see patterns in numbers, this question will present no challenge. If you are
having difficulty, don’t despair, you will find help in the following narrative.)
20. It is quite difficult to use the successive ionization energies to check if there are groups of electrons with the
same energy in a neutral atom because the measuring process produces an ion. Therefore, the forces
attracting the remaining electrons will be altered. For example, the first electron to be removed is attracted by
a net nuclear charge of 1+. The second electron is pulled away from a positive ion. When the second
electron is pulled, away there is a nuclear charge of Z+ surrounded by Z-2 electrons. The net nuclear charge
is 2+. The third electron to be removed would be attracted by a net nuclear charge of 3+. What would be the
net nuclear charge for the removal of the mth electron?
21. Thus even if two electrons had identical energies in the neutral atom their ionization energies would be
different. Use Coulombs Law to explain how this claim follows logically from the electrostatic argument
above.
22. If the attractive force didn’t increase each time an electron was removed then we could compare electron
energies on an equal basis. Suggest a way of eliminating the increase in the attractive force due to ion
formation. Show your reasoning.
23. Suggest a method for using successive ionization energies to determine an estimate of the energy of the
electrons in a neutral atom.
24. What assumptions are involved in your method?
Electron Arrangement
25. The increase in attractive force due to ion formation can be eliminated by dividing the successive ionization
energy by the charge on the ion formed. E1/1, E2/2, E3/3 and Em/m represent the energy required to remove the
first, second, third and mth electrons from a net nuclear charge of 1+. Explain why this is reasonable using
Coulomb’s Law. Thus, to compare electron energies on an equal basis we must compare E2/2, E3/3 and Em/in,
not the ionization energy by itself. Calculate the following Em/m for carbon. Obtain E1, E2, etc from IEII.XLS
(NOTE: If you haven’t converted the ionization energies in IEII.XLS into kJ/mol please do it now.)
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E1/1 = ______
E4/4 = ______
E2/2 = ______
E5/5 = ______
E3/3 = ______
E6/6 = ______
26. Which electrons have similar energies? ____________________________
E m / m , ( I o n iz a t io n E n e r g y ) / ( C h a r g e io n )
27. One way to show the arrangement of electrons in an atom is to write out the values for E 1/1 E2/2, etc. A
visual way of displaying the arrangement; makes use of an energy level graph. The energy to remove an
electron (Em/m) is plotted on the vertical axis. Small energy values are near the top of the axis. Large values
are near the bottom. This method of arranging the energy values places the most easily removed electrons
farthest from the nucleus. The electrons closest to the nucleus are the ones most strongly held. They require
the most energy to be removed. Thus by putting the large energy values nearest to the horizontal axis the
electrons most strongly held appear
Engery Level Diagram for Carbon
closest to the atomic number (nucleus)
or symbol of the element. Atomic
Em/m vs Z
number or the symbol of the element is
0
plotted on the horizontal axis. Plot the
values of E1/1, E2/2, etc for carbon on
2000
the axis system provided. Draw a box
around those energies that are very
4000
close to the same value. Draw an arrow
inside the box for each electron
6000
enclosed by the box. How many
8000
electrons are in the box corresponding
to the largest energy level? Which
10000
energy level (box) on the graph
corresponds to the electrons farthest
12000
from the nucleus? How many electrons
6C
are at this level? Describe the electron
Z, Atomic Number ---->
arrangement for carbon in words. Use
Coulomb’s Law to explain how this
arrangement provides an accurate visualisation of the arrangement of the electrons in a carbon atom.
28. If you haven’t already used Excel to calculate Em /m for all the ionization energies in IEII.XLS please do it
now. Plot energy level models for the first 10 elements on the graph on the next page.
29. Write the symbols for the elements below the corresponding atomic number on the graph.
30 Use the trends in the graph to predict the values of E7/7, E8/8 and E9/9 for neon. The experimental values to
the nearest 100 kJ/mol are: E7 = 20,000 kJ/mol, E8 = 23,100 kJ/mol, E9 = 115,400 kJ/mol.
From Graph
Em/m (kJ/mol)
Experimental
E7/7 =
E7/7 =
E8/8 =
E8/8 =
E9/9 =
E9/9 =
Em/m (kJ/mol)
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E m /m , Io n iza tio n e n e rg y/Io n C h a rg e
SSC & HLS CHEMISTRY - ChemPhys Systems
Topic 4.2 & 4.4 ATOMIC THEORY
Electron Arrangements
for the First 10 Elements
0
2000
4000
6000
8000
10000
12000
14000
0
1
2
3
4
5
6
7
Z, Atomic Number ---->
8
9
10
31. Compare the experimental values with the predicted values from your graph. (Originally these ionization energies for
neon were unknown but they have since been measured.) What does this comparison do to your confidence in the
energy level model for atoms?
32. The energy level or box closest to the horizontal axis is called the “1s level”. The second level or box up from
the horizontal axis is called the “2s level”. The third level is the “2p level” and the fourth level or box is called
the “3s level. Label all the levels on the graph. All “s” levels can hold the same number of electrons. How
many electrons are in the “s” levels? ________ All “p” levels hold the same number of electrons. How many
electrons are in the “p” levels? ________
33. Another test of the model you have created involves predicting energy levels for helium. Helium has only 2
electrons and unless helium was in an excited state both those electrons would be in the 1s energy level (
Em/m: 2,300 - 2,600 kJ/mol). When all the electrons are in the lowest energy levels that they can be, the atom
is said to be in the ground state. The electron configuration for helium described by He 1s2, with 2 electrons
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in the 1s energy level shows the electrons in the lowest energy level, the energy level closest to the nucleus.
However, if energy is added to helium gas some atoms may have the following electron configuration He * 1s1
2s1. In this configuration, the electrons are not in the ground state, one electron has been promoted to the 2s
energy level. In this excited state the atom is unstable and the electron will have a tendency to drop down to
the lower 1s energy just as water flows down hill. When the electron drops down to the 1s energy level it will
give off energy just as the water loses potential energy as it flows down hill. We will use the “Energy Level”
model to predict the energy helium would produce as it drops from an excited state to the ground state. Use
Excel to plot the Em/m versus Z for the first 10 elements. I know you have already done this but we need to
be a bit more precise in this activity than the graph on the previous page provided. On the vertical axis,
establish a scale for Em/m of 0 - 3,500. Plot the energy level diagrams for Z = 1 to 10. NOTE 1: The scale
will not accommodate the 1s electrons for elements beyond helium. NOTE 2: Use the average energy to plot a
single point when plotting energy levels for multiple electrons of similar energy values. NOTE 3: Use the
following to identify similar electrons, circle the 1s electron energy values, use a triangle to highlight the 2s
electrons and a square for the 2 p electrons. NOTE 4: Draw a vertical line parallel to the vertical axis at Z = 2
for Helium.
34. Once you have the energy level diagrams for the first ten elements plotted use Excel to create a trendline for
the 1s, 2s and 2p data sets. Extrapolate the 2s and 2p lines back until they meet the helium line. By
extrapolating the lines back to helium; you have predicted the 2s and 2p energy levels for helium. In the
ground state, He 1s2, there are no electrons in those energy levels so we can’t measure those energy levels
using successive ionization energies. Now all we have to do is imagine helium in an excited state e.g. He * 1s1
2p1. Since we know the electrons can only take on certain energies then the excited helium could return to the
ground state by only two paths. The electron could drop directly from the 2p to the 1s or it could drop from
the 2p to the 2s and then to the 1s. Assume that the electron follows the second path; use your graph to
determine the energy in kJ/mol that would be released. Don’t forget to explain how you did this. The amount
of energy given off is in the visible range. To calculate the wavelength of the light produced we will borrow a
couple of equations from Physics E = hf and c = f where “E” is the energy produced when the electron
drops from the 2p to the 2s energy level in kJ/atom, “h” is Planck’s constant, 6.625×10 -34 Js, “c” is the speed
of light, 2.998×108 m/s, “” is the wavelength of the light and “f” is the frequency of the light. NOTE: E is in
kJ/atom your graph is in kJ/mol. Use Excel to do your calculations.
35. Use the spectrum chart to determine the colour of the light you are predicting will be produced. Design an
experiment to check to see if your prediction is correct.
36. Compare your observations with your prediction. Does the visible spectrum for helium support or reject your
prediction. What evidence do you have that your “energy level” model is a good one? What does this
comparison do to your confidence in the energy level model for atoms?
37. The spectrum you observed had other colours than the one you predicted; use the energy level model to
explain how the other colours would be produced.
Using the Model to Explain Periodic Properties
38. Complete the electron arrangements for the alkali metals in the following table:
ELEMENT
NUMBER OF ELECTRONS
1s
2s
2p
3s
Li
Na
K
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39. Sodium, lithium and potassium are 3 alkali metals. They are all members of the same group in the periodic
table. Thus, they have the same combining power. Compare the electron arrangements of Li, Na, and K.
How are they the same? How do they differ?
40. Suggest a possible reason why Li, Na, and K have the same combing power and why the combining power is
one.
41. Complete the electron arrangements for the alkaline earth elements in the following table:
ELEMENT
NUMBER OF ELECTRONS
1s
2s
2p
3s
Be
Mg
Ca
42. Suggest a possible reason why Be, Mg, and Ca have the same combining power and why the combining
power is two.
43. Strontium and barium are two additional alkaline earth elements. What is their combining power? _______
44. For strontium and barium predict the number of outermost electrons and the type of level the outermost
electrons will be in.
45. Suggest a possible reason why the alkali metals and the alkaline earth metals have different combining
powers.
46. Complete the electron arrangements for the elements of the second period in the following table:
ELEMENT
NUMBER OF ELECTRONS
1s
2s
2p
3s
Be
B
C
N
0
F
Ne
47. Suggest a possible reason why combining power changes the way it does across a period.
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48. Based on your observation of the trends in electron arrangement for the 3 alkali metals, the 3 alkaline earth
metals and the elements of the second period explain why properties such as combining power, molar volume
and ionization energy are periodic functions of atomic number.
49. What has been the purpose of looking at the trends in electron arrangements in the alkali metals, alkaline earth
metals and the period two elements?
50. Explain why you are or why you are not confident in the electron energy level model of an atom you
developed. What additional evidence would you like to have?
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APPENDIX A:
CO-OPERATIVE LEARNING
Your task when working co-operatively with your peers is:

to be responsible for your own contribution and behaviour.

to be willing to help any group member who asks.

to ask for help from the teacher only when no one in your group can answer your question.

to raise questions when you don’t understand the content covered by the questions or you don’t understand how to
complete a task.

to ensure that everyone in your group can effectively answer questions about the content covered by the task.

to make sure that everyone in your team understands an answer to a given question and understands how to
complete a task.

to encourage others to share ideas, to give opinions or to help others.

to encourage the team to work hard and to stay on task.

to reflect on the co-operative skills you have learned/practised in this exercise. (See below for examples of cooperative skills.)
EXAMPLES OF CO-OPERATIVE SKILLS
TASK SKILLS
!
asking questions
WORKING RELATIONSHIP SKILLS
!
asking for clarification
!
acknowledging contributions
!
checking for others' understanding
!
checking for agreement
!
elaborating on others' ideas
!
disagreeing in an agreeable way
!
following directions
!
encouraging others
!
getting the group back to work
!
expressing support
!
keeping track of time
!
inviting others to talk
!
listening actively
!
keeping things calm/reducing tension
!
sharing information and ideas
!
mediating
!
staying on task
!
responding to ideas
!
summarizing/paraphrasing for
!
sharing feelings
understanding
!
showing appreciation
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Topic 4.2 & 4.4 ATOMIC THEORY
SSC & HLS CHEMISTRY - ChemPhys Systems
GROUP EVALUATION FORM
Please fill out this form together.
1. We checked to make sure we understood directions.
Always
-----+-----+-----+-----|-----+-----+-----+-----
Never
2. We shared our individual work and remembered to take turns.
Always
-----+-----+-----+-----|-----+-----+-----+-----
Never
3. We helped one another.
Always
-----+-----+-----+-----|-----+-----+-----+-----
Never
4. We praised one another.
Always
-----+-----+-----+-----|-----+-----+-----+-----
Never
5. We listened without interrupting.
Always
-----+-----+-----+-----|-----+-----+-----+-----
Never
We Liked:
Signatures:
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Topic 4.2 & 4.4 ATOMIC THEORY
We Wished:
Date:
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