electromagnetic radiation to end



Activity 1.10 Form a group and discuss the following questions, then present your responses to the whole class. 1. Explain how energy travels in space. 2. What is the importance of electromagnetic radiation (EMR) in chemistry? 3. What are the common features of different energy sources?

CHEMISTRY GRADE 11

16 UNIT 1

In 1873, James Clerk Maxwell proposed that light consists of electromagnetic waves. According to his theory, an electromagnetic wave has an electric field and magnetic field components. These two components vibrate in two mutually perpendicular planes (Figure 1.6). EMR is the emission and transmission of energy in the form of electromagnetic waves.

Figure 1.6: The electric field and magnetic field components of an electromagnetic waves Electromagnetic waves have three primary characteristics: wavelength, frequency and speed. Wavelength(λ, Greek lambda), is the distance the wave travels during one cycle (Figure 1.7). It is expressed in meters (m) and often, for very short wavelengths, in nanometers (nm), picometers (pm), or angstrom (Å). Frequency (ν, Greek letter nu) is the number of cycles the wave undergoes per second and is expressed in units of l/second (1/s; also called hertz, Hz).

Figure 1.7: Frequency of waves

Electromagnetic Radiation and Atomic Spectra

17 UNIT 1

Wave has a speed which depends on the type of wave and the nature of the medium through which it is traveling (for example, air, water, or a vacuum). The speed (c) of a wave is the product of its wavelength and its frequency: c = vλ (1.1) In a vacuum, electromagnetic waves travel at 3 ´ 108 m/s, which is a physical constant called the speed of light. EMR comes in a broad range of frequencies called the electromagnetic spectrum (Figure 1.8). A rainbow is an example of a continuous spectrum. Different wavelengths in visible light have different colors from red (λ = 750 nm) to violet (λ = 380 nm).Radiation provides an important means of energy transfer. For instance, the energy from the Sun reaches the Earth mainly in the form of visible and ultraviolet radiation. The glowing coals of a fireplace transmit heat energy by infrared radiation. In microwave ovens, microwave radiation is used to heat water in foods, causig the food to cook quickly.

Figure 1.8: The electromagnetic spectrum

CHEMISTRY GRADE 11

18 UNIT 1

Example 1.3 Ethiopian National Radio, Addis Ababa station broadcasts its AM signal at a frequency of 2400 kHz. What is the wavelength of the radio wave expressed in meters? Solution: We obtain the wavelength of the radio wave by rearranging Equation 1.1

so,

8

6 3.00 1 0 m/ s = = 125.0 m 2.4 10 s c v λ × = ×

Exercise 1. 4 1. The most intense radiation emitted by the Earth has a wavelength of about 10.0 µm. What is the frequency of this radiation in hertz? 2. Addis Ababa Fana FM radio station, broadcasts electromagnetic radiation at a frequency of 98.1 MHz. What is the wavelength of the radio waves, expressed in meters?

 



Why are waves treated as particles? In 1900, Max Planck, the German physicist, came to an entirely new view of matter and energy. He made a revolutionary proposal, energy like matter is discontinuous.

According to Planck, atoms and molecules could emit or absorb energy only in discrete quantities, like small packages or bundles. Each of these small “packets” of energy is called a quantum. The energy of a quantum is proportional to the frequency of the radiation. The energy Eof a single quantum is given by:

E = hν (1.2) Where h is called Planck’s constant and ν is the frequency of radiation. The value of Planck’s constant is 6.63 ´ 10-34 J. s.

Electromagnetic Radiation and Atomic Spectra

19 UNIT 1

Since ν = c/λ,Equation 1.2 can also be expressed as:

hcE= λ

(1.3)

According to quantum theory, energy is always emitted or absorbed in integral multiples of hν;for example, hν, 2hν, 3hν, etc. A system can transfer energy only in whole quanta. Thus, energy seems to have particulate properties.

Example 1.4 The blue color in fireworks is often achieved by heating copper (I) chloride (CuCl) to about 1200 °C. Then the compound emits blue light having a wavelength of 600 nm. What is the increment of energy (the quantum) that is emitted at 600 nm by CuCl? Solution: The quantum of energy can be calculated from the Equation 1.2: E = hv The frequency (ν) for this case can be calculated as follows:

8 -1

-7

15 -1 3.0 × 10 ms = 6.0 × 10 m =0.5 × 10 s

c v =

λ

So, E = hv = 6.63 × 10-34 J.s × 0.50 × 1015s-1 = 3.315 × 10-19 J = 19 3.32 1 0 J −×

The Photoelectric Effect In 1905, Albert Einstein used the quantum theory to explain the photoelectric effect. The photoelectric effect is a phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency, called the threshold frequency, νo.

CHEMISTRY GRADE 11

20 UNIT 1

These observations can be explained by assuming that EMR is quantized (consists of photons), and the threshold frequency represents the minimum energy required to remove the electron from the metal’s surface. Photons are particles of light or energy packet. The minimum energy required to remove an electron is: Eo = hνo (1.4) Where Eo is the minimum energy (of the photon), and νo, the threshold frequency. A photon with energy less than Eo (ν < νo)cannot remove an electron, or a light with a frequency less than the νo produces no electrons. On the other hand, if a light has ν > νo, the energy in excess of that required to remove the electron is given to the electron as kinetic energy (KE): KEe = ½ mv2 = hν - hνo (1.5) Where KEe is the kinetic energy of an electron, m is mass of an electron, v is the velocity of an electron, hν, is the energy of an incident photon, and hνo is the energy required to remove an electron from the metal’ssurface. Intensity of light is a measure of the number of photons present in a given part of the beam: a greater intensity means that more photons are available to release electrons (as long as ν > νo for the radiation). In his theory of relativity in 1905, Einstein derived the famous equation: E = mc2 (1.6) Rearranging this equation, we have 2 Em c = (1.7) Where E is energy, m is mass, and c is speed of light. The main significance of Equation 1.7 is that energy has mass. Using this equation, we can calculate the mass associated with a given quantity of energy or the apparent mass of a photon. For electromagnetic radiation of wavelength, λ, the energy of each photon is given by the expression: photon hc E = λ (1.8)

Electromagnetic Radiation and Atomic Spectra

21 UNIT 1

Then, the apparent mass of a photon of light with wavelength is given by: ( ) 22 hc Eh m = = = ccc λ λ (1.9) We can summarize the important conclusions from the work of Planck and Einstein as follows: Energy is quantized. It can occur only in discrete units called photon or quanta. EMR, which was previously thought to exhibit only wave properties, seems to show certain characteristics of particulate matter as well. This phenomenon is sometimes referred to as the dual nature of lightand is illustrated Figure 1.9.

Figure 1.9: The dual nature of light

Example 1.5 1. Compare the wavelength for an electron (mass = 9.11 × 10-31 kg) traveling at a speed of 1.00 × 107 m/s with that for a ball (mass = 0.10 kg) traveling at 35 m/s. Solution: We use the equation m = h/cλ, Where h = 6.63 × 10-34 J.s = 6.63×10-34 kg. m2.s Since 1 J = 1 kg. m2/s2 For the electron:

34 663 10 kg . − ×

λ=

2

31

ms

911 10 kg

..

. − × 7 ms 100 10 . ××

11 728 10 m 728nm = . . − ×= For the ball: 34 6.63 10 kg −× λ= 2 .m .s 0.10 kg 35 m/s × 34 25 1.89 10 m m 189 10 n −− = × = ×

CHEMISTRY GRADE 11

22 UNIT 1

2. The maximum kinetic energy of the photoelectrons emitted from a give metal is 1.5 × 10–20 J when a light that has a 750 nm wavelength shines on the surface. Determine the threshold frequency, νo , for this metal. Calculate the corresponding wavelength, λo. Solution: a) Determination of the threshold frequency, νo Solve for v from c = v ´ λ Thus, v = c/λ = (3.0 ´ 108 m/s)/7.5 ´ 10-7 m) = 0.4 ´ 1015 s-1 = 4.0 ´ 1014 s-1 Similarly, rearrange Equation 1.5 and solve vo

o = hv KEv h −

34 14 1 –20

34 6.63 10 J.s 4.0 10 s 1.5 10 J 6.63 10 J. s −− − × × × − × ×

=

20 –20 20

34 34 26.52 10 J 1.5 10 J 24.02 10 J = 6.63 10 J. s 6.63 10 J.s −− −− × − × × ××

=

14 1 3.77 10 s− = × Therefore, a frequency of 3.77 ´ 1014 Hz is the minimum (threshold) required to cause the photoelectric effect for this metal. b) Calculate the corresponding wavelength λo:

8

14 -1

-6 3.0 × 10 m s = 3.77 × 10 s 0.796 × 10 m 796 nm ° c = v = = λo

Electromagnetic Radiation and Atomic Spectra

23 UNIT 1

Exercise 1.5 1. The following are representative wavelengths in the infrared, ultraviolet, and -ray regions of the electromagnetic spectrum, respectively: 1.0 ´ 10-6 m, 1.0 ´ 10-8 m, and 1.0 ´10-10 m. a. What is the energy of a photon of each radiation? b. Which has the greatest amount of energy per photon? c. Which has the least? 2. A clean metal surface is irradiated with light of three different wavelengths λ1, λ2, and λ3. The kinetic energies of the ejected electrons are as follows: λ1: 7.2 ´ 10-20 J; λ2: approximately zero; λ3: 5.8 ´ 10-19 J. Which light has the shortest wavelength and which has the longest wavelength? Determine the threshold frequency, νo, for this metal. 3. The minimum energy required to cause the photoelectric effect in potassium metal is 3.69 ´ 10-19 J. Will photoelectrons be produced when visible light, 520 nm and 620 nm, shines on the surface of potassium? What is or are the velocities of the ejected electron/s?

 

Activity 1.11 Discuss the following ideas in pairs and share with the rest of the class. 1. Why do you observe different colors when you are watching fireworks? 2. As it is shown in the Figure 1.10, when compounds of the alkali metals: lithium, sodium, and potassium are excited in the gas flames they give different colored flames. Why do they emit different colors?

Figure 1.10: Flame colors of lithium, sodium, and potassium compounds

CHEMISTRY GRADE 11

24 UNIT 1

Atomic or line spectra are produced from the emission of photons of electromagnetic radiation (light). Different kinds of spectrum are observed when an electric discharge, or spark, passes through a gas such as hydrogen. The electric discharge is an electric current that excites, or energizes, the atoms of the gas. More specifically, the electric current transfers energy to the electrons in the atoms raising them to excited states. The atoms then emit the absorbed energy in the form of light as the electrons return to lower energy states. When a narrow beam of this light is passed through a prism, we do not see a continuous spectrum, or rainbow, as sunlight does. Rather, only a few colors are observed, displayed as a series of individual lines. This series of lines is called the element’s atomic spectrum or emission spectrum. The wavelengths of these spectral lines are characteristic of the element producing them, and used for their identification. For example, the emission (line) spectrum of hydrogen atom is show in Figure 1.11.

Figure 1.11: The hydrogen line spectrum, containing only a few discrete wavelengths

Changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of emitted light, as shown in Figure 1.12. For example, a given change in energy from a high to a lower level would give a wavelength of light which can be expressed using Planck’s equation: ∆E = hν = hc/λ

Electromagnetic Radiation and Atomic Spectra

25 UNIT 1

Figure 1.12: A change between two discrete energy levels emits a photon of light

 



Activity 1.12 Form a group and discuss the following questions. Share your ideas with the rest of the class. The nature of the nucleus of the atom was explained by Rutherford. However, he was not able to explain the position and velocity of electrons in the atom. 1. Is it possible to know the exact location of an electron in the atom? Defend your suggestion. 2. Explain why an electron does not enter the nucleus, even though they are oppositely charged. In 1913, Niels Bohr (a Danish physicist) explained why the orbiting electron does not radiate energy as it moves around the nucleus. He introduced the fundamental idea that the absorption and emission of light by hydrogen atoms was due to energy changes of the electrons within the atoms. The fact that only certain frequencies are absorbed or emitted by an atom tells us that only certain energy changes are possible. Thus, energy changes in an atom are quantized.

CHEMISTRY GRADE 11

26 UNIT 1

Bohr used Planck’s and Einstein’s ideas about quantized energy and proposed the following assumptions: 1. The electron in an hydrogen atom travels around the nucleus in a circular orbit. 2. The energy of the electron in an atom is proportional to its distance from the nucleus. The further an electron is from the nucleus, the more energy it has. 3. Only limited number of orbits with certain energies are allowed. This means, the orbits are quantized. 4. The only orbits that are allowed are those for which the angular momentum of the electron is an integral multiple of h/2π. 5. As long as an electron stays in a given orbital, it neither gains or losses energy. That means, the atom does not change its energy while the electron moves within an orbit. 6. The electron moves to a higher energy orbit only by absorbing energy in the form of light, and emitting light when it falls to a lower energy orbit. The energy (photon) of the light absorbed or emitted is exactly equal to the difference between the energies of the two orbits. Furthermore, Bohr showed that the radii, r, of the permitted orbits or energy levels for an atom of hydrogen atom are related to Planck’s constant, h, the electron’s charge, e, and its mass, m. Consider hydrogen atom with an electron with constant speed, v, circulating the nucleus in an orbit of radius, r. The total energy of the electron is the sum of the kinetic energy (energy of movement) and the potential energy (energy of position):

2

21 2 + eE mv r = (1.10) For an electron to exist in a stable orbit of a constant radius, the centripetal force (attracting the electron to the nucleus), e2/r2, and the centrifugal force (pulling away the electron from the nucleus),mv2/rmust be equal:

22 2 e mv rr = (1.11) Bohr then introduced an additional requirement that the angular momentum, mvr, of the electron can take only certain permitted values, that is, an integral multiple of h/2π. This requirement is called a quantum condition:

Electromagnetic Radiation and Atomic Spectra

27 UNIT 1

2 nhmvr = π

(1.12)

Solving Equation 1.12 for v gives: nhv = 2 mr π

(1.13)

Substituting for v in Equation 1.11 and solving for r gives:

44

22 2 2 22 n h h r = = n me me   ππ 

(1.14)

Here, n is positive integer (n = 1, 2, 3 . . .) and is called quantum number. It is known that h, π, m, and e are constants, thus Equation 1.14 can be simplified to: r = n2 ao (1.15) According to Equation 1.15 the only permitted values of the radii of the electron path in the hydrogen atom are those proportional to the square of a whole number,n. The numerical values of ao is 0.53 Å. Thus, r = (0.53 Å)n2 For instance, for n = 1, r = 0.53Å. This is the first Bohr radius. The larger the values of n, the further the electron from the nucleus.

Figure 1.13: Bohr’s energy levels of a hydrogen atom

CHEMISTRY GRADE 11

28 UNIT 1

Bohr showed that the energies that an electron in hydrogen atom can occupy are given by: H 2-n RE n = (1.16) Where RH, the Rydberg constant for the hydrogen atom and has the value 2.18 x 10-18 J. Thus, Equation 1.15 can be written as:

18

n 2 2.18 × 1 0 JE n − =− The negative sign in Equation 1.16 is an arbitrary convention, signifying that the energy of the electron in the atom is lower than the energy of a free electron, which is an electron that is infinitely far from the nucleus. The energy of a free electron is given a value of zero. As the electron gets closer to the nucleus (as n decreases), En becomes larger in absolute value, but also more negative. The most negative value, then, is reached when n = 1, which corresponds to the most stable energy state. We call this the ground state or ground level,which refers to the lowest energy state of an atom. The stability of the hydrogen electron diminishes for n = 2, 3.... Each of these levels is called an excited state, or excited level, which is higher in energy than the ground state. A hydrogen electron for which n is greater than 1 is said to be in an excited state. Using Bohr’s Equation 1.16, relating the energy (En ) and energy level (n) for an electron it is possible to calculate the energy of a single electron in a ground state or excited state, or the energy change when an electron moves between two energy levels.

Electromagnetic Radiation and Atomic Spectra

29 UNIT 1

Example 1.6 Consider the n = 5 state of hydrogen atom. Using the Bohr model, calculate the radius of the electron orbit, the velocity and the energy of the electron. Solution: To determine the radius, Equation 1.15 is used: ( ) 2 0.53 Å 5 15.24 Å 1.524 nmr = × = = Velocity of the electron is determined using Equation 1.13: = 2 nhv mrπ

34 5 6.63 × 1 0 kg − = ( ) 1 31 2 m s 2 × 3.14 × 9.11 × 1 0 kg − − 9 × 1 .524 × 1 0 m −

5 3.8 1 0 m/s = × Equation 1.16 is used to solve E5 18

20

5 2 2.18 × 1 0 J 8.72 × 1 0 J 5 E − −= −= Calculate the energies of the hydrogen electron in n = 1, n = 2 and n = 3 Solution: Using Equation 1.16:

18

18

1 2 2.18 10 JFor = 1, 2.18 1 0 J 1 nE − −× =− = − × 18 19 2 2 2.18 10 J 5.54 10 J 2 n = 2, E − −× = − = − × 18 19 3 2 2.18 10 J3 2.42 10 J 3 n , E − −× = = − = − × Bohr’s model also quantitatively explained the line spectra of hydrogen atom. He proposed that the absorptions and emissionsin line spectra correspond to the transfer of the electron from one orbit to another. Energy must be absorbed for the electron to move from one orbit to another one having a bigger radius. Whereas, energy is emitted when an electron moves from the higher orbital energy level, ni, to the lower orbital, nf,energy level. Thus, the change in energy, E,is the difference in the energy between the final and the initial state electron:

CHEMISTRY GRADE 11

30 UNIT 1

fi EEE ∆ = − (1.17) This equation is similar to:

H 22 fi

18

22 fi

11

11 2.18 × 1 0 J

ER nn

nn

−

 ∆ =− −   =−−   (1.18)

Where ni and nf represent quantum numbers for initial and final states respectively. But, ∆E = hν, thus we have:

18

22 fi 11 = 2.18 1 0 JE hv nn −  ∆ = − × −  (1.19) Notice that when nf > ni, ∆E is positive, indicating that the system has absorbed energy. But, ni > nf, ∆E is negative and this corresponds to emission of energy.

Example 1.7 Calculate the energy emitted when an electron moves from the n = 3 to the n = 2 energy level. Determine the wavelength of the emitted energy. Solution: Equation 1.19 is used, to determine the emitted energy:

18 19 22 11 2.18 10 J 3.03 1 0 J 23 E −−  ∆ =− × − = ×   To obtain λ, Equation 1.19: hcE hv ∆ = = λ

Thus,

34 8

19 m6.63 × 1 0 J s × 3.0 × 1 0 s 3.03 1 0 J

hc E

− −= = ∆× 76.56 × 1 0 m 656 nm −= =

Electromagnetic Radiation and Atomic Spectra

31 UNIT 1

Exercise 1.6 1. What is the wavelength of a photon (in nanometers) emitted during a transition from the n = 5 state to the n = 2 state in the hydrogen atom? 2. Calculate the frequency of the green line arising from the electron moving from n = 4 to n = 20 in the visible spectrum of the hydrogen atom using Bohr’s theory.

Each spectral line in the emission spectrum corresponds to a particular transition in a hydrogen atom. When we study a large number of hydrogen atoms, we observe all possible transitions and hence the corresponding spectral lines. For instance, Figure 1.14 illustrates line spectra of a hydrogen atom when its electron moves from n = 4 to n = 1; n = 3 to n = 1 and n = 2 to n = 1.

Figure 1.14: The emission spectrum of a hydrogen atom Each horizontal line represents an allowed energy level for the electron in a hydrogen atom. The energy levels are labeled with their principal quantum numbers. The emission spectrum of hydrogen includes a wide range of wavelengths from the infrared to the ultraviolet. Table 1.2 shows the series of transitions in the hydrogen spectrum; they are named after their discoverers. The Balmer series was particularly easy to study because some its lines fall in the visible range.

CHEMISTRY GRADE 11

32 UNIT 1

Table 1.2: The various series in atomic hydrogen emission spectrum Series nf ni Spectrum region Lyman 1 2, 3, 4, … Ultraviolet Balmer 2 3, 4, 5, … Visible and ultraviolet Paschen 3 4, 5, 6, . . . Infrared Brackett 4 5, 6, 7, . . . Infrared

For a larger orbit radius (i.e. a higher atomic energy level), the further the electron drops, the greater is the energy (higher v, shorter λ) of the emitted photon. Exercise 1.7 1. Calculate the energies of the states of the hydrogen atom with n = 2 and n = 3, and calculate the wavelength of the photon emitted by the atom when an electron makes a transition between these two states. 2. What is the wavelength of a photon emitted during a transition from the ni = 10 state to the nf = 2 state in the hydrogen atom?

 



The Bohr Model was an important step in the development of atomic theory. He introduced the idea of quantized energy states for the electron in a hydrogen atom. The model explains atoms and ions containing only one electron such as H, He+ and Li2+. However, the model has several limitations: • It doesn't explain the atomic spectra of more complicated atoms and ions, even that of helium, the next simplest element. • It doesn't explain about further splitting of spectral lines in the hydrogen spectra on application of a magnetic field. • It considers electrons to have both known radius and orbit, which is impossible according to Heisenberg's uncertainly principle.

Electromagnetic Radiation and Atomic Spectra

33 UNIT 1

 



 Bohr’s model assumed that an atom has only certain allowable energy levels in order to explain the observed line spectrum. However, his assumption had no basis in physical theory. In 1924, Louis de Broglie, the French physicist, proposed a surprising reason for fixed energy levels: if energy is particle-like, perhaps matter is wavelike. De Broglie reasoned that if electrons have wavelike motion and are restricted to orbits of fixed radii that would explain why they have only certain possible frequencies and energies. By combining Einstein’s equation for the quantity of energy equivalent to a given amount of mass (E = mc2) with Planck’s equation for the energy of a photon (E = hν = hc/λ), de Broglie derived an equation for the wavelength of any particle of mass, m, whether a planet, ball, or electron-moving at speed, v. h mv = λ (1.20) According to this Equation 1.20, matter and energy show both wave and particulate properties. The distinction between a particle and a wave is only meaningful in the macroscopic world, it disappears at the atomic level. This dual character of matter and energy is known as the wave-particle duality.

Example 1.8 Calculate the de Broglie wavelength of an electron that has a velocity of 1.00 × 106 m/s. (electron mass, me = 9.11 × 10–31 kg; h = 6.63 × 10–34 J.s).

Solution:

2

34

6 31e

m 6.63 1 0 kg s m 1.00 1 0 9.11 1 0 kg s h mv − − × = = × × × λ 9 0.73 1 0 m 0.728 nm − = × = What is the speed of an electron that has a de Broglie wavelength of 1.00 nm

Solution:

e

34 6.63 10 kgh v m −× = = λ 1 2 9 3 m s 1.00 10 9.11 10 m kg −− × × ×

65 mm 0.728 1 0 7.28 10 ss = × = ×

CHEMISTRY GRADE 11

34 UNIT 1

Exercise 1.8 1. What is the characteristic wavelength of an electron (in nm) that has a velocity of 5.97 ´ 106 m/s (me = 9.11 ´ 10–31 kg)? 2. Calculate the wavelength (in nanometers) of an H atom (mass = 1.67 ´ 10-27 kg) moving at 7.00 ´ 102 cm/s. 3. Calculate the wavelength (in nm) of a photon emitted when a hydrogen atom undergoes a transition from n = 5 to n = 2.

1.6 

At the end of this section, you will be able to: ) state Heisenberg's uncertainty principle ) describe the significance of electron probability distribution. ) explain the quantum numbers n, l, ml, ms ) write all possible sets of quantum numbers of electrons in an atom. ) describe the shapes of orbitals designated by s, p and d.

Activity 1.13 Form a group and discuss the following questions, then present your responses to the rest of the class. 1. If particles have wavelike motion, why can’t we observe its motion in the macroscopic world? 2. If electrons possess particle nature it should be possible to locate electrons. How can an electron be located? 3. Is there any wave associated with a moving elephant?

The Bohr model of an electron orbiting around the nucleus, looking like a planet around the Sun, doesn't explain properties of atoms. The planetary view of one charged particle orbiting another particle of opposite charge does not match some of the best-known laws of classical physics.

The Quantum Mechanical Model of the Atom

35 UNIT 1

Scientists have developed quantum mechanics, which presents a different view of how electrons are arranged about the nucleus in the atom. This view depends on two central concepts: the wave behavior of matter and the uncertainty principle. The combination of these two ideas leads to a mathematical description of electronic structure.

 

 Discovery of the wave properties of matter raised a new and very interesting question. If a subatomic particle can exhibit the properties of a wave, is it possible to say precisely where that particle is located. A wave, extends in space, so its location is not defined precisely. In 1827, Werner Heisenberg, the German physicist, proposed the Heisenberg uncertainty principle, stating that it is not possible to know with great certainty both an electron’s position and its momentum p (where p = mν) at the same time. Heisenberg was able to show that if ∆p is the uncertainty in the momentum and ∆x is the uncertainty of the position of the electron, then:

( )( ) ( ) ( ) or 44 ∆ ∆ ≥ ∆ ∆ ≥ ππ hh x p x mv This equation shows that if we measure the momentum of a particle precisely (i.e., if ∆pis very small), then the position will be correspondingly less precise (i.e, ∆xwill become larger). In simpler terms, if we know precisely where a particle is, we cannot know precisely where it has come from or where it is going. If we know precisely how a particle is moving, we cannot know precisely where it is. The Heisenberg uncertainty principle has no practical consequence in everyday objects in the macroscopic world. However, it has very significant consequences when applied to atomic and subatomic particles.

CHEMISTRY GRADE 11

36 UNIT 1

 

The quantum mechanical description of the atom is based on the assumption that there are waves associated with both matter and radiations. The mathematical description of such wave provides information about the energy of electrons and their position. Erwin Schrödinger (1927), suggested that an electron or any other particle exhibiting wavelike properties can be described by a mathematical equation called a wave function (denoted Greek latter psi, ψ). The equation is very complex. However, it leads to series of solutions that describe the allowed energy states of electrons. The square of a wave function, ψ2, gives the probability of finding an electron in a certain region of a space. The results of a quantum mechanics indicate that the electron may be visualized as being in a rapid motion within a given region of space around the nucleus. Although we cannot determine the precise position of an electron, the probability of the electron being at a definite location can be calculated. The region in which an electron is most likely found is called an orbital. The electron may occupy anywhere within an orbital at any instant in time. So, an electron can be considered as a particle that can rapidly move from place to place, behaving like an “electron cloud” whose density varies within the orbital. In quantum mechanics, each electron in an atom is descried by four quantum numbers. Three of the quantum numbers specify the wave function that gives the probability of finding an electron at various place in spaces. The fourth one is used to describe the spin (magnetic property) of the electrons that occupy the orbitals. The four quantum numbers are: 1. The principal quantum number (n) describes the main energy level, or shell, an electron occupies. It may be any positive integer, n = 1, 2, 3, 4, etc. It describes the size and energy of the shell in which the orbital resides and it is analogous to the energy levels in Bohr’s model. 2. The angular momentum quantum number (ℓ) designates the shape of the atomic orbitals. Within a shell different sublevels or subshells are possible, each with a characteristic shape. It takes values from 0 to n-1. Orbitals of the same n, but

The Quantum Mechanical Model of the Atom

37 UNIT 1

different ℓ are said to belong to different subshells. It is also called azimuthal quantum number or subsidiary quantum number. A given energy level, n, has n2 total number of orbitals. For example, in n = 4, ℓ has values of 0, 1, 2, and 3. Each value of ℓ corresponds to an orbital label and an orbital shape. The following letters are usually used to denote the values of ℓ: Value of ℓ Corresponding subshell 0 s 1 p 2 d 3 f

Example 1.9 What do “4” and “d” represent in 4d? Solution: The number 4 gives the principal quantum number (n = 4) and the letter d gives the type of orbital (ℓ = 2). 3. The magnetic quantum number (mℓ)is also called the orbital-orientation quantum number. It has integral values between -ℓ and ℓ, including 0. The value of mℓ is related to the orientation of the orbital in space relative to the other orbitals in the atom. The number of possible mℓ values or orbitals for a givenℓvalue is 2ℓ + 1. 4. The electron spin quantum number (ms) refers to the spin of an electron and the orientation of the magnetic field produced by this spin. For every set ofn, ℓ, and mℓ values, ms can take the value +½ or -½. Each atomic orbital cannot accommodate more than two electrons, one with ms = +½ and another with ms = -½.

CHEMISTRY GRADE 11

38 UNIT 1

Exercise 1.9 1. What are the values of n and ℓ for the following subshells? a. 1s c. 4s e. 4f b. 3p d. 3d 2. Write the subshell notations that correspond to a. n = 3 and ℓ = 0 c. n = 7 and ℓ = 0 b. n = 3 and ℓ = 1 d. n = 3 and ℓ = 2

Example 1.10 1. What are the allowed values of the quantum numbers through n = 2? Solution: The allowed quantum number values in n = 2 are: n ℓ mℓ ms Electron capacity of subshell 4ℓ + 2 Electron capacity of shell 2n2 1 0 (1s) 0 +½, -½ 2 2 2 0 (2s) 0 +½, -½ 2 8 2 1(2p) -1, 0, 1 ±½ for each value of mℓ 6 8 2. What values of the angular momentum quantum number (ℓ) and magnetic quantum number (mℓ) are allowed for a principal quantum number, n = 3? How many orbitals are allowed for n = 3? Solution: Determining ℓ values: For n = 3, ℓ = 0, 1, 2 Determining mℓ for each ℓ value: For ℓ = 0, mℓ = 0 For ℓ = 1, mℓ = –1, 0, +1 For ℓ = 2, mℓ = –2, –1, 0, +1, +2 Number of orbitals in n = 3 is n2 = 32 = 9 orbitals These orbitals are: 3s: 1 orbital 3p: 3 orbitals 3d: 5 orbitals Total = 9 orbitals

The Quantum Mechanical Model of the Atom

39 UNIT 1

Exercise 1.10 1. What are the allowed values of the quantum numbers through n = 4? 2. Write an orbital designation corresponding to the quantum numbers: a. n = 4, ℓ = 2, mℓ = 0 c. n = 5, ℓ = 1, mℓ = -1 b. n = 3, ℓ = 1, mℓ = 1 d. n = 4, l = 3, mℓ = -3 3. What values ℓ and mℓ are allowed for a principal quantum number (n) of 3? How many orbitals are allowed for n = 3? 4. Can an orbital have the quantum number n = 2, ℓ = 2, mℓ = 2 5. For an orbital with n = 3 and mℓ = 1, what is (are) the possible value(s) ℓ? 6. Which of the following orbitals do not exist: 1p, 2s, 2d, 3p, 3d, and 3f?

 





The three-dimensional aspects of the orientation of the atomic orbitals are usually represented by drawing a boundary surface diagram that encloses the highest probability (about 90%) of the total electron density in an orbital. Figure 1.15, shows that the region of the greatest probability of finding an s electron is in a spherically symmetrical space whose origin is the atomic nucleus. The 1s orbital is the smallest, the 2s orbital is larger than 1s and so on. Regardless of their principal quantum numbers, all s orbitals are spherical.

Figure 1. 15: The threeS-orbitals

CHEMISTRY GRADE 11

40 UNIT 1

The p orbitals of any principal quantum number are arranged along three mutually perpendicular axes, x, y, and z, so that the region of the highest electron density are in dumb bell-shaped boundary surface (Figure 1.16). The three p orbitals are designated as px, py andpz.

Figure 1. 16: The three p - orbitals

Two lobes of each p orbital lie along a line with the nucleus at their center. For instance, the three 2porbitals are classified as 2px, 2py and 2pz Higher principal energy levels (n > 3) have five d orbitals in addition to, one sorbital, three 3p orbitals. The special orientations of d orbitals are much more complex in shape than p orbitals. Figure 1.17 shows the different distribution of the five d atomic orbitals.

Figure 1.17: The five d orbitals

Electronic Configurations and Orbital Diagrams

41 UNIT 1

The principal energy level whose values are n ≥ 4 have additional fourth sublevels. For instance, in n = 4, there are a 4s subshell with one orbital, a 4p subshell with three orbitals, a4dsubshell with five orbitals, and a 4f subshell with seven orbitals. The f orbitals have more complex shapes than the d orbitals. 1.7 



At the end of this section, you will be able to: ) explain the Aufbau Principle ) explain Pauli's Exclusion Principle ) explain Hund’s Rule ) write ground state electron configurations of multi-electron atoms.

Activity 1.14 Form a group and discuss the given questions. Then, share your ideas with the rest of the class. 1. Why dosen't an atomic orbital hold more than two electrons? 2. Why do you think that electrons in an atom could not occupy the spaces between the main energy levels? Several questions arise when you look carefully at the electron configuration of an atom. To answer these questions, it is necessary to know the basic principles governing the distribution of electrons among atomic orbitals. The electron configuration for any atom is governed by the following three principles: 1. Aufbau (building up) Principle: This is a scheme used to reproduce the electron configurations of the ground state of atoms by successively filling with electrons in a specific order (the building up order). In general, electrons occupy the lowest-energy orbital available before entering the higher energy orbital. Accordingly, the ground state electron configurations of atoms are obtained by filling the subshell in the following order; 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, and so on, as indicated in Figure 1.18.

CHEMISTRY GRADE 11

42 UNIT 1

Figure 1.18: The order of filling orbitals 2. Hund’s Principle: Equal energy orbitals (degenerate orbitals) are each occupied by a single electron before the second electrons of opposite spin enters the orbital. In other words, each of the three 2porbitals (2px, 2py and 2pz) will hold a single electron before any of them receives a second electron. 3. Pauli’s Exclusion Principle: No two electrons can have the same four quantum numbers. That means, they must differ in at least one of the four quantum numbers.

 



 

The electronic configuration of an atom describes the distribution of the electrons among atomic orbitals in the atom. Two general methods are used to denote electron configurations. The subshell (sublevel) notation uses numbers to designate the principal energy levels and the letters s, p, d and f to identify the sublevels. A superscript number following a letter indicates the number of electrons (e) in the designated subshell. The designation can be written as nle. For instance, the ground state electron configuration of H (Z =1) is 1s1.

Electronic Configurations and Orbital Diagrams

43 UNIT 1

Activity 1.15 Form a group and discuss the reason why the notation nle does not include electron spin quantum numbers. (Where n, l and e are principal quantum number, azimuthal quantum number and number of electrons, respectively). The other way to present this information is through an orbital diagram, which consists of a rectangular box (or circle, or just a line) for each orbital available in a given energy level, with an arrow indicating the electron’s presence and its direction of spin. Traditionally, ↑ represents, ms = +½whereas ↓ designates ms = -½. The orbital diagrams for the first ten elements are:

1s2 2s2 2p5

1s2 2s2 2p3

1s2 2s2 2p1

1s2 2s1 2p

Li(Z=3)

B(Z=5)

N(Z=7)

F(Z=9)

Be(Z=4)

C(Z=6)

O(Z=8)

1s2 2s2 2p6

1s2 2s2 2p4

1s2 2s2 2p2

1s2 2s2 2p

H(Z=1)

1s1

He(Z=2)

1s2

Ne(Z=10)

The three orbitals in the 2psublevel are degenerate (have equal energy) and have the same n and ℓ values), thus, the fifth electron of boron can go into any one of the 2p orbitals. Since a p sublevel has ℓ = 1, the mℓ (orientation) values can be –1, 0, or +1. For convenience, the boxes are labeled from left to right, –1, 0, +1, and assume it enters the mℓ = –1 orbital: n = 2, ℓ = 1, ml = –1, and ms = +½.

The three 2porbitals have equal energy, but they can be along the x, y, or z axes.

CHEMISTRY GRADE 11

44 UNIT 1

Activity 1.16 Discuss the following questions in groups, and share your ideas with the rest of the class. 1. What does each box in an orbital diagram represent? 2. What are the similarities and differences between a 1s and a 2s orbital? 3. What is the difference between a 2px and a 2py orbital? 4. What is the meaning of the symbol 4d6?

Exercise 1.11 1. Write the expected electron configuration for these atoms: a. Na (Z= 11) d. V (Z = 23) b. Al (Z = 13) e. Mn (Z =25) c. P (Z =15) f. Fe (Z = 26) 2. Indicate the total number of: a. p electrons in N (Z = 7) c. 3d electrons in S (Z = 16) b. s electrons in Si (Z = 14) 3. Indicate which of the following sets of quantum numbers in an atom are unacceptable and explain why: a. (1, 0, ½, ½) d. (2, 2, 1, +½) b. (3, 0, 0, +½) ` e. (4, 3, -2, +½) c. (3, 2, 1, 1)

For Li, the first 2 electrons occupy the 1s orbital, and the third electron must occupy the first orbital with n = 2, the 2sorbital. Thus, the electron configuration for Li is 1s22s1. To avoid writing the inner-level electrons, this configuration is often abbreviated as [He] 2s1, where [He] represents the electron configuration of He, 1s2. Similarly, Mg (Z =12), has the configuration1s22s22p63s2, or [Ne] 3s2. Then the next six elements, aluminium to argon, have configurations obtained by filling the 3p orbitals one electron at a time. Table 1.3 shows the ground state electron configurations of some atoms.

Electronic Configurations and Orbital Diagrams

45 UNIT 1

Table 1.3: Ground state electron configurations of some atoms Atom Atomic number (Z) Electron configuration H He Be O Ne Cl Ar Ca Sc Cr 1 2 4 8 10 17 18 20 21 24 1s1 1s2 1s22s2 or [He]2s2 1s22s22p4 or [He]2s22p4 1s22s22p6 or [He]2s22p6 1s22s22p63s23p5 or[Ne] 3s23p5 1s22s22p63s23p6 or[Ne] 3s23p6 1s22s22p63s23p64s2 or[Ar] 4s2 1s22s22p63s23p64s2 3d1or[Ar] 4s23d1 1s22s22p63s23p64s1 3d5 or[Ar] 4s13d5

Notice that in the electron configuration of an atom, the electrons in the outermost principal quantum level of an atom are called valence electrons. For example, the valence electrons of the Be atom, are the 2s electrons. For the Ne atom, the valence electron is the electrons are in the 2s and 2p electrons. Valence electrons are the most important electrons to chemists since they are involving in bonding, as you will learn in the next chapter. The inner electrons are known ascore electrons. Examine the electron configurations of chromium and copper. The expected configurations, those based on the Aufbau principle, are not the ones observed through the emission spectra and magnetic properties of these elements. Expected Observed Cr (Z = 24 ) [Ar]4s23d4 [Ar]4s13d5 Cu (Z = 29 ) [Ar]4s23d9 [Ar]4s13d10 The reason for these exceptions to the Aufbau principle are not completely understood, but it seems that the half-filled 3d subshell of chromium (3d5) and the fully filled 3d subshell of copper (3d10) lends a special stability to the electron configurations. Apparently, having a half-filled 4s subshell and a half-filled 3d subshell gives a lower energy state for a Cr atom than having a filled 4s subshell.

CHEMISTRY GRADE 11

46 UNIT 1

Because there is little difference between the 4s and 3d orbital energies, expected and observed electron configurations are quite close in energy. At higher principal quantum numbers, the energy difference between certain subshell is even smaller than that between the 3d and 4s subshells. As a result, there are still more exceptions to the Aufabu principle among the heavier transition elements.

Activity 1.17 Form a group and complete the following table for the first-row transition metals on your note book: Element Atomic number Ground state electron configuration Condensed electron configuration Sc 21 Ti 22 V 23 Cr 24 Mn 25 Fe 26 Co 27 Ni 28 Cu 29 Zn 30

Electronic Configurations and the Periodic Table of the Elements

47 UNIT 1

1.8 

 

 

At the end of this section, you will be able to: ) correlate the electron configurations of elements with their positions in the periodic table ) give a reasonable explanation for the shape of the periodic table ) classify elements as representative, transition and inner-transition elements ) explain the general trends in atomic radius, ionization energy, electron affinity, electronegativity, and metallic character of elements within a period and group of the periodic table ) write the advantages of the periodic classification of elements.

 



Activity 1.18 In your Grade 9 chemistry lessons, you have learned about the development of the modern periodic table. Form a group and discuss the following questions, then present your responses to the whole class. 1. How is today’s periodic table different from the one that Mendeleev published? 2. What is a “period?” What does it represent? 3. What is a “group?” What does it represent? 4. How does the electron configuration of an element give information about the period and group it is in? 5. Why are some elements placed out of the main body of the periodic table?

CHEMISTRY GRADE 11

48 UNIT 1

Elements are arranged in the modern periodic table in a specific pattern that helps to predict their properties and to show their similarities and differences. Periodic relationships can be summarized by the general statement called the periodic law. In its modern form, the periodic law states that certain sets of physical and chemical properties repeat at regular intervals (periodically) when the elements are arranged according to increasing atomic number.

 



Activity 1.19 Answer the following questions in groups and present your responses to the whole class. 1. What is the importance of classifying elements in groups and periods? 2. What could be the basis of classifying elements? 3. Why are there two different numbering systems for groups? 4. Which sublevel is being filled in period 1? The periodic classification follows as a logical consequence of the electronic configuration of atoms. Elements are grouped according to their outer-shell electron configurations, which account for their similar chemical behavior. The period indicates the value of n for the outermost or valence shell. There are 18 groups and 7 periods in the modern periodic table. A metalloid is an element that has properties that are between those of metals and non-metals, for example boron, germanium and silicon.

Electronic Configurations and the Periodic Table of the Elements

49 UNIT 1

Project 1.1

Form a group of five and do the following activities and submit a report both in word and PDF formats. The elements can be divided into representative, transition, and inner transition elements based on the type of subshell being filled. Discuss these different classes of elements by searching information from the internet or any other sources. Also, identify each block in the blank periodic table.

 

Activity 1.20 Discuss the following questions in groups and, present your responses to the whole class. 1. How does size of elements vary across a period? 2. Why are elements of Groups 1 (IA) and 2 (IIA) called metals, while those of Group 17 (VIIA) non-metals? 3. Why are elements of Group 18 (VIIIA) least reactive? The electron configurations of the atoms display a periodic variation with increasing atomic number (nuclear charge). As a result, the elements show periodic variations of physical and chemical behavior. In this section you will examine some periodic atomic properties like atomic radii, ionization energies, electron affinities, electronegativity, and metallic character.

CHEMISTRY GRADE 11

50 UNIT 1

Atomic Size (Atomic Radii)

Activity 1.21 Answer the following questions in groups, then present your responses to the whole class. 1. Why don't the sizes of atoms increase uniformly with increasing atomic number? 2. In which location in the periodic table would you expect to find the elements having the largest atoms? Explain. 3. How do the sizes of atoms change: a. from left to right in a row in the periodic table? b. from top to bottom in a group in the periodic table? Explain. Exact size of an isolated atom cannot be measured because the electron cloud surrounding the atom does not have a sharp boundary. However, an estimate of the atomic size can be made by measuring the distance between the nuclei of two adjacent atoms. This property is called the atomic radius. One of the most common methods to determine the atomic radius is to assume that atoms are spheres touching each other when they are bonded together (Figure 1.19).

Figure 1.19: Atomic radius for a diatomic molecule.

2 dr = Atomic size varies within both a group and a period of the main-group elements. These variations in atomic size are the result of two opposing influences: changes in the principal quantum number (n) and changes in the effective nuclear charge ( Zeff ) the nuclear charge an electron actually experiences. The net effect of these depends on the shielding of the increasing nuclear charge by the inner electrons