Chemistry

Key unit Competence

To relate Bohr’s atomic model with atomic spectrum of Hydrogen, write electronic configuration of atoms and ions using s, p, d and f atomic orbitals and interpret graphical information related to ionization energy of elements.

Learning objectives

By the end of this unit, I will be able to:

•Explain the stability of atoms using the concept of quantization of energy.

•Explain the achievements and limitations of Bohr’s atomic model.

•Explain the existence of energy levels using the data from emission spectra.

•Describe hydrogen spectral lines and spectral line series

•Explain the types of spectra in relation with the nature of light

•Explain the quantum theory of the atom using the quantum numbers.

•Determine the number and shapes of orbitals in given level or principal quantum number

•Explain the rules governing the electronic configuration: Aufbau principle and Hund’s rule

•Explain the relationship between the electronic configuration and the stability of the atoms

•Interpret the graphs of first ionisation energy against the atomic number.

•Describe the factors which influence the first ionisation energy.

2.1. Bohr’s atomic model and concept of energy levels

The potential energy of a person walking up ramp increases in uniform and continuous manner whereas potential energy of person walking up steps increases in stepwise and quantized manner. This can be explained by the values of energy which are continuous for the person walking up ramp while they are discrete (discontinued) for the person walking up steps (Figure 2.1(a) and Figure 2.1(b).

Niels Bohr (1885-1962) a young Danish physicist working in Rutherford’s laboratory, suggested a model for the hydrogen atom and predicted the existence of line spectra. In his model, based on Planck’s and Einstein’s ideas about quantized energy, Bohr proposed three postulates:

•An electron can rotate around the nucleus in certain fixed orbits of definite energy without emission of any radiant energy. Such orbits are called stationary orbits.

•An atom can make a transition from its stationary state of higher energy E2 to a state of lower energy E1 and emit a single photon of frequency ν. Conversely, an atom can absorb an energy at the lower level E1 and transit to the higher energy level E2. That is, the change in energy for a system which can be represented by the equation:

where n is an integer (1,2,3,...) and h is Planck’s constant

determined from experiment and has a value of 6.626x10-34J.s; ⱱ is the frequency of the electromagnetic radiation absorbed or emitted. Each of these small “packets” of energy is called photon also called quantum of energy. Energy can be gained or lost only in whole-number multiples of the quantityνh,That is, the change in energy for a system can be represented by the equation:, where n is an integer (1,2,3,...).

An atom does not release energy when it is in one of its stationary states. That is, the atom does not change energy while the electron moves on a given orbit. When an electron on a given orbit absorbs an appropriate quantum of energy, it jumps, i.e. is promoted to a higher energy orbit; this process is called “excitation”of electron. On the contrary, if the electron loses an appropriate quantum of energy, it falls on the lower energy orbit by emission of a light corresponding to the lost quantum of energy and the process is called “de-excitation” of electron. As there are many energy levels on which electrons can be excited and de-excited, an atom will have many lines of absorption, each corresponding to a quantum of energy absorbed: this appears as a series of lines called absorption spectrum. In the same way the series of emission lines will produce an emission spectrum (see Fig. 2.4).

2.1.1. Achievements of Bohr’s Atomic Model

• Explanation of the stability of an atom

Based on Rutherford’s atomic model, the electrons move around the nucleus in circular paths called orbits. According to the classical theory of electromagnetism, a charged particle revolving around a charged nucleus would release energy and end up by spiraling into the nucleus; thus the atoms would be unstable. The Bohr’s atomic model makes an assumption of discreet orbit (allowed orbit) to explain why an atom is stable; by doing so, Bohr introduces the concept of quantization of energy. Bohr’s atomic model explains the origin of atomic absorption and emission spectra.

• Explanation of the production of the absorption and emission spectra

The Bohr’s atomic model explains the origin of atomic absorption and emission spectra.

2.1.2. Limitations of Bohr Model

1.Bohr’s theory fails to explain the origin of the spectral lines of multi-electron atoms.

It only explains the origin of the spectrum of hydrogen-like species having only one electron such as H, He+, Li2+, Be2+, ........

The model fails to explain the spectral lines of atoms or species with more than one electron.

2. According to Bohr, the circular orbits in which electrons revolve are planar. However, modern research has shown that an electron moves around the nucleus in the three dimensional space.

3. Bohr’s theory fails to account for Zeeman Effect and Stark Effect. Zeeman Effect is the splitting of the spectral lines into thinner and closely- spaced lines when an excited atom is placed in a magnetic field. Stark Effect consists of the splitting of the spectral lines into thinner and closely-spaced lines in presence of electric field.

4. Bohr’s theory is in contradiction with Heisenberg’s uncertainty principle. Bohr assumes that the electron revolves around the nucleus in circular orbits at fixed distance from the nucleus and with a fixed velocity. However, according to W. Heisenberg, it is not possible to know simultaneously the accurate position and the velocity of a very small moving particle such as an electron.

Checking up 2.1

1. Find out two more examples that you can use to illustrating the concept of quantization.

2. Discuss the main weakness of Rutherford’s nuclear atom.

2.2. Hydrogen spectrum and spectral lines

Activity 2.2

Look at the picture of neon tube light below and do research about how this neon tube light works to produce light and present your findings

Bohr’s atomic model allows to explain the emission spectra of atoms. This happens when excited electrons lose energy in form of electromagnetic radiation and fall to lower energy levels.

The wave-particle nature of the light

Light as a waveThe light is a wave-like phenomenon as shown in Figure 2.2.

It is characterized by its wave length, generally symbolized by the Greek letter lambda, λ, and its frequency, represented by the Greek letter nu1, ν.

As shown in the Figure below, the wavelength represents the distance between two successive summits/peaks (or two successive troughs).The frequency represents the number of complete wavelengths made by the light per second, also called cycles per second.

Visible light is composed by different visible lights with different λ and ν.

But all those lights have the same speed, the speed of light, which, in a vacuum, is equal to: 3.00x108 m/s; although different types of light have different λ and ν, they move at the same speed c. This results in the relation between the speed of light and its wavelength and frequency: c = νλFrom this relation, and since c is constant, we can conclude that:

•Light with long wavelength has low frequency, whereas

•Lights with short wavelength has high frequency.

Let’s take an example to illustrate: light1 has λ1 equal to 105m whereas light2 has λ2 equal to 10-5 m. After 1 second, both would have travelled 3.00x108m, the speed of light, but their frequencies will be different:

ν1 = c/λ1 = 3.00x108ms-/105m = 3.00x103s-= 3,000 cycles/s

v2 = c/λ2= 3.00x108ms-/10-5m= 3.00x1013s-= 30,000,000,000,000 cycles/sLight is energy, represented by: E = hν where h is Plank’s constant (h=6.626x10-34Js)

Hence energy in the light is proportional to its frequency; higher the frequency of the light, higher is its energy and vice-versa.

The different colors of the visible light differ by their wavelength as shown in the

As illustrated in Figure 2.2 below, the right side of the spectrum consists of high-energy, high-frequency and short wavelength radiations. Conversely, the left side consists of low-energy, low-frequency and long wavelength radiations.

The letter gamma, γ, may also be used.

When an electron is excited or de-excited, the energy absorbed or emitted corresponds to the difference of energy, ΔE, between the final energy level of the electron, E2, and the starting energy level of the electron, E1: E2 – E1 = ΔE = hν. ΔE is positive when E2>E1, this is the case of absorption and excitation of electron; on the other hand ΔE may be negative when E2<E1, in case of emission and de-excitation of electron.

Figure 2.4 below shows the different series of emission spectra of hydrogen. As you can see, the difference between those series is the final energy level where the electron fall after de-excitation.

The series have been named according to the scientists who discovered them.

Ionization of an atom or loss of an electron corresponds to excitation of an electron to the level n=∞.

Checking2.2

1. What is the meaning of infinity level in the hydrogen spectral lines?

2. Given a transition of an electron from n=5 to n=2. Calculate energy

ii) Frequency

iii) Wavelength

2.3. Atomic spectra

Activity 2.3

Observe the picture above, discuss in groups and answer the following questions.

a. What do you see on the above photo?

b. State the physical phenomenon which is related to the above photo.

c. Think of any other means of producing the same pattern. List two of them.

d. What property can you attribute to light with reference to the above process?

Checking up 2.3

1. Different metals, when exposed to a flame, emit different flame colors. Explain the origin of that difference.

2. Would you expect to see the emission rays and the absorption rays of a given element to appear at the same place of a photographic plate or not. Explain your answer.

3. How do you explain the many spectral rays for the same element?

2.4 Orbitals and Quantum Numbers

Activity 2.4

1. a)Write the electronic configuration of aluminium atom(Z=13)

b) Indicate the number of electrons in each energy level/quantum shell

c) The shells are numbered from inside-outward starting from 1, 2, 3, 4 ... which other name is given to these shells?

d) How did you obtain the exact number of electrons in each energy level/quantum shell in (c) above?

We have seen the weakness and critics against the atomic Bohr’s model. In order to answer to the questions not answered by that model, other atomic models were proposed. One of those models is the Quantum model that has been developed by the Austrarian physicist Erwin Schrödinger (1887-1961). The model is based on a mathematical equation called Schrödinger equation. This model is based on the following assumptions or hypotheses:

•An electron is in continuous movement around the nucleus but cannot be localized with precision; only the high probability of finding it in a cartain region around the nucleus can be known.

•The region where the probability of finding electron is high, at more than 95%, is called “orbital”; in other words, the orbital is the volume or the space (tridimensional) around the nucleus where there is a high probability of finding the electron.

Without going into the mathematical development of the Schrödinger equation, we can say that the energy of the electron depends on the orbital where it is located. And an atomic orbital is described by a certain number of “quantum numbers”

according to the solution of Schrodinger equation, i.e. 3 whole numbers:

1) The principal quantum number is a positive integer which varies from 1 to ∞.

The principal quantum number indicates the energy level in an atom where electrons can be located: the higher the n value, the higher the energy level. An electron in energy level n=1 has lowest energy in an atom. The principal quantum number, n, has been traditionally given names by the letters: K(n=1), L(n=2), M(n=3), N(n=4), O(n=5), P(n=6).

In the Bohr’s atomic model, K, L, M, ... were used to represent different orbits or shells of electrons. Later on, the term shell sometimes is used to describe a group of orbitals with the same principal quantum number. The term subshell describes a group of orbitals with the same principal and second quantum number. The maximum number of orbitals and electrons that can be found in an energy level n are n2and 2n2, respectively (Table 2.1). The maximum number of sub shells in an energy level n equals n.

Table 2.1 Relation between the principal quantum number, the number of orbitals and the maximum number of electrons.

2)The angular momentum quantum number (l)

The second quantum number is the angular quantum number represented by the letter, l: it is an integer which can take any value from zero or higher but less than n-1, i.e. equal to: 0,1, 2, 3,....up to n-1. For example if n= 1, l is equal to 0, if n= 2, l can be 0, 1. It is also called secondary or azimuthal quantum number. It indicates the shape of the orbital and is sometimes called the orbital shape quantum number. By tradition, those different shapes of orbitals have been given names or letter symbols: l = 0 = s, l =1 = p, l = 2 = d, l=3 = f

3) Magnetic quantum number (ml)

The magnetic quantum number describes the orientation of the orbital. It is an integer that varies from -l to +l. For example if: l = 0, ml can only be 0; if l = 1, ml = -1, 0, +1; if l=2, ml = -2, -1, 0, 1, 2. As you can see for each value of l there are (2l+ 1) values of ml corresponding to (2l + 1) orientations under the influence of magnetic field. The s orbital where l is zero and ml has no orientation; it has the shape of a sphere as shown in

Table 2.2: Relationship between the n, l and ml

The table 2.2 shows that, apart s sub-level that has only one orbital, other sub-levels have a certain number of different orbitals; those orbitals have the same energy but differ in their specific orientations. Example p orbitals are 3 with different orientations: pxpypz.

Different sub-levels belonging to the same principal quantum number have different energies as follows: s < p < d < f

4) The spin quantum number (S)

The fourth quantum number is the spin quantum number, represented by the symbol S (or ms in some books). The electron behaves as a spinning magnet.The spin quantum number is the property of the electron, not the orbital.This number describes the spinning direction of the electron in a magnetic field. The direction could be either clockwise or counterclockwise. The electron behaves as if it were spinning about its axis, thereby generating a magnetic field whose direction depends on the direction of the spin. The two directions for the magnetic field correspond to the two possible values for the spin quantum number, S (ms). Only two values are possible: s = +1/2 and -1/2 as shown in the Figure 2.7 below.

ms = +1/2 and ms = -1/2 are commonly represented by ↑ and ↓ respectively.In conclusion an electron in any given atom is decribed by 4 quantum numbers: (i) three quantum numbers which describe the orbital where the electron is located: n, l and ml and (ii) one quantum number describing the spin of the electron, S or ms.

2.5 Electronic configuration of atoms and ions

Activity 2.5

1. Write the electronic structure of the following chemical speciesK (Z=19), Ne (Z=10), Al3+ (Z=13), Cl (Z=17), O2- (Z=16)

2. Using information in question 1,

a. Determine the group and period of K and Cl.

b.Which species have a stable electronic configuration? Explain.

The electron configuration is the distribution of electrons of an atom in its atomic orbitals. The electronic configuration of an atom is governed by three main rules.

1) Aufbau Principle

The Aufbau principle explains how to build the electronic configuration of an atom.The Aufbau principle states that atomic orbitals of lower energy must be filled before the higher energy orbitals. The Aufbau principle is referred to as the “building-up” principle.

According to that principle, if an atom has only one electron, this electron will occupy the lowest principal quantum energy level, n=1, and the lowest energy orbital in that principal quantum energy, i.e. l = 0 = s. This is represented as: 1s1, meaning one electron in s orbital of the 1st energy level. If the atom has 2 electrons, the second electron will be filled in the same s orbital to give the structure 1s2.

Note the way of notation: the first number indicates the principal energy level or principal quantum number, followed by the letter indicating the orbital, followed by the number of electrons present in the orbital, as super-script.

2) Pauli Exclusion Principle

What happens if we have 3 electrons in an atom? Can we squeeze them in 1s orbital?

There is a principle called Pauli Exclusion Principle states: in an atom, two electrons cannot have the four quantum numbers n, l, ml, and S(ms) identical. This explains why the two electrons in the same orbital must have their spin opposite:

                                                            

The Pauli exclusion principle doesn’t allow us to put a 3rd electron in the same orbital, since if we put 3 electrons in the same orbital, 2 electrons will have 4 identical quantum numbers and this is not allowed

                                                                  

In other words, the Pauli Exclusion Principle is telling us that you cannot put more than 2 electrons in an orbital. i.e. the maximum number of electrons in an orbital is 2.

Hence, the 3rd electron must go in energy level n = 2, since energy level n=1 if full; it has only one orbital s. Then for that atom with 3 electrons, the electronic structure is: 1s22s1

3) Hund’s rule

Atom with 4 electrons: 1s22s2

Atom with 5 electrons: 1s22s22p1

What about an atom with 6 electrons? Are we putting the 6th electron in the same orbital as the 5th electrons? Remember that there are 3 p orbitals pxpypz of the same energy!

The Hund’s rule answers to that question.

It states that orbitals of equal energy are each occupied by one electron before electrons begin to pair up into the same orbital. By convention, all the unpaired electrons are given the same orientation spin. A slight preference for keeping electrons in separate orbitals helps to minimize the natural repulsive forces that exist between two electrons.

Therefore, atom with 6 electrons: 1s22s22px1py1pz0

When building the electronic configuration of elements, you must be guided by the principles and rules seen above and: writing the principal quantum number in Arabic number, followed by the orbitals immediately followed by the number of electrons in the orbital as superscript.

An atom X: 1s2: has only two electrons in s orbital at the 1st energy level

An atom Y: 1s22s22p3: has electrons in 2 levels of energy: level n=1, and level n= 2. In level 1, it has 2 electrons in s orbital. In level 2, it has 2 electrons in s orbital and 3 electrons in p orbitals.

Figure 2.8 is a useful and simple aid for keeping track of the order in which electrons are first filled for each atomic orbital. The different orbitals are filled in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.Notice that as energy levels increase starting from n=3, 4s orbital is filled before 3d, 5s before 4d, etc... as shown in the diagram below. But when ionized, 4s electrons are ionized before 3d, and 5s before 4d.

Checkup 2.5 (a)

1. Build the electronic configuration of the following atoms: 1H, 3Li, 5B, 11Na, 18Ar,19K, 21Sc, 24Cr, 26Fe, 29Cu

2. Write the electronic configuration for each of the following pairs of ions. State the more stable ion in gaseous state and explain your choice.

a. cu+ and cu2+

b.Fe2+ and Fe3+

Expanded notation

Expanded notation is another method of writing the s, p, d and f notation. The method uses the same concept as s, p, d and f notation except that each individual orbital of a sub-level having many orbitals is represented with a subscript letter indicating the orientation of the orbital. This applies for p, d, and f orbitals. Considering that p-orbital has three componentsxp,ypand pz, the expanded electronic configuration of some elements is given hereafter.

Checkup 2.5 (b)

Write the expanded electronic configuration for each of the following atom/ions. S(z=16), P3-(z=15), Mg2+(z=12)

Orbital box representation

An orbital box representation consists of a box for each orbital in a given energy level, grouped by sublevel, with an arrow indicating an electron and its spin.

Note that two electrons in the same orbital have necessarily opposite spins as indicated in the examples below.

The table 2.4 shows the electronic configuration of some elements using orbital box representation and applying Hund’s rule.

Table 2.4: Electronic configuration using orbital box representation

Checkup 2.5(c)

Using boxes to represent orbitals, draw the electronic configuration ofN3- (z=7), Ti4+(z=22), Mg2+(z=12), Ar(z=18)Identify the isoelectronic species that are present.

Noble Gas Notation

All noble gases have completely filled subshells and can be used as a shorthand way of writing electron configurations for subsequent atoms.When using this method, the following steps are respected.

a. Identify the noble gas whose electronic configuration is included in that of the concerned element.

b.Write the chemical symbol of the identified noble gas within square brackets. We call this the noble gas core.

c. Add electrons beyond the noble gas core. Note that electrons that are add-ed to the electronic level of the highest principal quantum number (the outermost level or valence shell) are called valence electrons.

Example: Given the electronic configurations of the noble gases Ne and Ar, one can write the electronic configuration of some elements in noble gas notation of some elements as:

Checking up 2.5 (d)

Using the noble gas notation, write the electronic configuration of the following atoms/ions.

a. Ge (Z=32)

b. S (Z=16)

c. Co2+ (Z=27)

d. Br- (Z=35)

e. Sr (Z=38)

2.6. Relationship between ionization energy, energy levels and factors influencing ionization energy

Activity 2.6

Write the electronic configuration of the following elements/ions, use s, p, d, ...)

Sodium, magnesium, magnesium ion (Mg2+), aluminium, aluminium ion (Al3+), oxygen ion (O2-)

Identify the common feature of ions in (1) and why do they have such feature

Suggest what happened to aluminium atom when it changed to aluminium ion (Al3+)

Identify the group and the period of aluminium, sodium and oxygen atom

2.6.1. Concept of Ionization energy

The ionization energy is a measure of the energy needed for an atom, in gaseous state, to lose an electron and become positive ion.

The first ionisation energy is the energy required to remove one electron from an atom in its gaseous state. The example below shows how to represent the successive ionization energies of an atom M.

Second ionisation energy and nth ionisation energy: Two or more electrons can be removed and we have successive ionization energies.

The ionization energy is usually expressed in kiloJoules per mole (kJ.mol-1). This energy is required to overcome the attractive force between the nucleus and the electron and then remove the electron. Theoretically there are as many successive ionisation energies as there are electrons in the original atom. In figure 2.9, someone can make an interpretation of successive ionization energies of an atom

2.6.2. Interpretation of a graph of successive ionization energies of an atom

The graph shows that the energy to remove electron increases as more electrons are successively removed.

a) The energy required to remove the first electron is relatively low. This corresponds to the loss of one 3s electron.

b) To remove the second electron needs greater energy because this electron is closer to the nucleus in a 2p orbital. There is a steady increase in energy required as elec-trons are removed from 2p and then 2s-orbitals.

c) The removal of the tenth and eleventh electrons requires much greater amounts of energy, because these electrons are closer to the nucleus in 1s orbital.

2.6.3. Factors influencing the extent of ionization energy

The ionization energy is a physical property of elements that can be influenced by some factors:

1) Size of atom

The atomic size is the distance between the nucleus and valence shell. As the number of energy levels (shells) increases, the force of attraction between nucleus and valence electron decreases. Therefore, the valence electrons are loosely held to the nucleus and lower energy is required to remove them, i.e. ionization energy decreases with increase in atomic size and vice versa.This is what happens when you go down a Group.

2) Nuclear charge

The nuclear charge is the total charge of all the protons in the nucleus. As the nuclear charge increases, the force of attraction between nucleus and valence electrons on the same valence energy level increases and hence makes it difficult to remove an electron from the valence shell. The higher the nuclear charge, the higher the ionization energy. This is what happens when you cross a period from left to right.

3) Screening effect or Shielding effect

The Screening effect or Shielding effect is due to the presence of inner electrons which have a screening or shielding effect against the attraction of the nucleus towards the outermost electrons. The electrons present in inner shells between the nucleus and the valence shell reduce the attraction between nucleus and the outermost electrons. This shielding effect increases with the increasing number of inner electrons. A strong Shielding effect makes it easier to remove an external electron and hence lowers the ionisation energy.

2.6.4. Importance of ionization energy in the determination of the chemistry of an element

Ionization energy provides a basis to understand the chemistry of an element. The following information is provided.

Determination of metallic or non- metallic character.

The I.E informs us how the atom will behave chemically: a low I.E indicates that the element behaves as metal whereas a high I.E indicates that the element behaves as non-metal.

The first ionization energies of metals are all nearly below 800kJ mol-1 while those of non- metals are all generally above 800 kJ mol-1.

Down the group ionization energies decrease so that the elements became more metallic. In groups 14 and 15 there is change from non metallic to metallic character. Across a period from left to right 1st I.E. increases. The elements become less metallic to non- metallic.

Example: The first three ionization energies for elements A, B, C, and D are given in the table below

This table shows that for a given element: 1st IE < 2nd IE < 3rd IE.

From the 1st I.E. of the elements it can be predicted that elements B and C have typical metallic properties since their 1st ionization energies are low.

D is expected to be non-metal because of its high 1st IE.

Checking up 2.6

1. Given elements: Cl, Ca, and Na and the following 1st IE: 456, 578.8 and 1251 KJ/mol. Respectively.Match those 1st IE with the three element and justify.

2. Given elements: bromine and iodine and 1st IE: 1008 and 1140 KJ/mol. Which 1st IE correspond to which element? Explain.

3. Explain why 2nd IE is always greater than the 1st IE?

2.7. End unit assessment

1. Which of the following is the correct representation of the ground-state electron configuration of molybdenum? Explain what is wrong with each of the others.

2. Which of the following electron configurations are correct and which ones are wrong? Explain.

3. Photosynthesis uses 660 nm light to convert CO2 and H2O into glucose and O2. Calculate the frequency of this light.

4. Which of the following orbital designations are incorrect: 1s, 1p, 7d, 9s, 3f, 4f, 2d?

5. The data encoded on CDs, DVDs, and Blu-ray discs is read by lasers. What is the wavelength in nanometers and the energy in joules of the following lasers?

6. Concerning the concept of energy levels and orbitals,

a. How many subshells are found in 3=n?

b. What are the names of the orbitals in 3=n?

c. How many orbitals have the values 4=nand3=l?

d. How many orbitals have the values 23==,lnand2−=lm?(e) What is the total number of orbitals in the level4=n?

7. A hypothetical electromagnetic wave is pictured here. What is the wavelength of this radiation?

8. Consider the following waves representing electromagnetic radiation:

a. Which wave has the longer wavelength?

b. Calculate the wavelengths of the two radiations

c. Which wave has the higher frequency and larger photon energy?

d. Calculate these values.

9. Order the orbitals for a multielectron atom in each of the following lists according to increasing energy:a. p5 ,d5b. s4, p3c. s6,d4

10. According to the Aufbau principle, which orbital is filled immediately after each of the following in a multielectron atom?

a. 4s

b. 3d

c. 5f

d. 5p

11. According to the Aufbau principle, which orbital is filled immediately be-fore each of the following?

a. 3p

b. 4p

c. 4f

d. 5d

12. Four possible electron configurations for a nitrogen atom are shown be-low, but only one represents the correct configuration for a nitrogen atom in its ground state. Which one is the correct electron configuration? Which configurations violate the Pauli Exclusion Principle? Which configurations violate Hund’s rule?

13. Explain the variation in the ionization energies of carbon, as displayed in this graph.

14. The first seven ionization energies of an element W are shown below

What factors determine the magnitude of the first ionization energy