Chapter 6 electronic structure of atoms
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Broad outcomes Understand the wave nature of light and explain relationships between frequency, wavelength and speed of light Explain Planck’s quantum theory and its relevance in explaining the photoelectric effect Explain the Bohr model of the atom and its use to interpret line spectra

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Chapter 6 electronic structure of atoms l.jpg

  • Broad outcomes

  • Understand the wave nature of light and explain relationships between frequency, wavelength and speed of light

  • Explain Planck’s quantum theory and its relevance in explaining the photoelectric effect

  • Explain the Bohr model of the atom and its use to interpret line spectra

  • Understand the wave behavior of matter and uncertainty principle

  • Describe and represent atomic orbitals using quantum numbers diagrams

  • Describe the effect of nuclear charge on the energies of orbitals in many electron atoms

  • Describe the evidence of electron spin and explain the Paul Exclusion principle

  • Understand how electrons are finally arranged in atoms

  • Understand how electron configurations relate to the periodic table

Chapter 6:Electronic Structure of Atoms


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6. 1 Wave nature of light

  • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.

  • The distance between corresponding points on adjacent waves is the________________


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Wave nature of light

  • The number of waves passing a given point per unit of time is the _____________________

  • For waves traveling at the same velocity, _____________________________________

Which has higher

Frequency ?


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Electromagnetic radiation (EMR)

  • Visible light is part of electromagnetic radiation

  • Since EMR carries energy through space, is called radiant energy

  • All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s.

  • Therefore, c = ______

  • Where c is speed of light (m/s) ,  is the wavelength (metres), and  is the freguency in cycles per second or per second (Hertz)

  • Different properties of EMR is due to different wavelength


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Electromagnetic Radiation (EMR)

Electromagnetic spectrum?

EMR arranged in order of increasing wavelength


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Practice exercise

A laser used in eye surgery to fuse detached retina produces radiation with wavelength of 640.0 nm.

(a) Calculate the frequency of this radiation

(b) An FM radio station broadcasts electromagnetic radiation at frequency of 103.4 MHz. MHz = 106s-1

(a)

(b)

4.688 x 1014 s-1

2.901 m


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6.2 Quantized energy and photons

  • The wave nature of light does not explain how an object can glow when its temperature increases.

  • Max Planck explained it by assuming that energy comes in packets called ________

  • E = _______

  • Matter emit or absorb energy only in whole numbers of h, 2h, 3h called quanta of energy


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6.2.2 Photoelectric effect and photons

  • Einstein used this assumption (Planck`s) to explain the photoelectric effect.

  • He concluded that energy is proportional to frequency:

    E = h

    where h is Planck’s constant, 6.63  10−34 J-s.


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The Nature of Energy

  • Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: How ?


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Practice exercise

  • A laser emits light with a frequency of 4.69 x 1014 s-1. What is the energy of one photon of the laser?

  • If a laser emits a pulse of energy containing 5.0 x 1017 photons of this radiation, what is the total energy of the pulse?

  • If the laser emits 1.3 x 10-2 J of energy during a pulse, how many photons are emitted during the pulse?

    (a) 3.11 x 10 -19 J (b) 0.16 J (c) 4.2 x 1016 photons


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6.3 Line spectra and Bohr Model

  • Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

  • Most sources of radiation emit different wavelengths called spectrum

  • Spectrum consists of continuous spectrum like rainbow


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6.3 Line spectra and Bohr Model

  • One does not observe a continuous spectrum, as one gets from a white light source.

  • Only a line spectrum of discrete wavelengths is observed.


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6.3 Line spectra and Bohr Model

  • Equation for wavelength of line spectra given by Rydberg equation

1

1

n12

1

n22

=

RH

-

λ

Where RH is 1.096776 x 10 7 m -1, n1 and n2 are positive

integers, n2 > n1

This equation could work but not fully explained.


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Line spectra and Bohr Model

  • Niels Bohr adopted Planck’s assumption and explained these phenomena of line spectra in this way:

    • Electrons in an atom can only occupy certain orbits (corresponding to certain energies).


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Line spectra and Bohr Model

  • Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

  • Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

    E = h


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1

nf2

( )

-

E = −RH

1

ni2

Line spectra and Bohr Model

The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron.


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1

n2

( )

E = −hcRH

1

ni2

Line spectra and Bohr Model

Modified equation by Bohr of energy of hydrogen atom

n : 1 to ∞ principle quantum numbers which corresponds to different orbitals

Energy levels in the H atom from Bohr model

1

nf2

J ( )

-

E = h۷= hc/λ = −2.18 x 10-18


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h

mv

 =

6.4 The Wave Nature of Matter

  • Louis de Broglie positulated that if light can have material properties, matter should exhibit wave properties.

  • He demonstrated that the relationship between mass and wavelength was

mv is also referred to momentum


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Practice exercise

Calculate the velocity of neutron whose de Broglie wavelength is 500pm. The mass of the neutron is given in the table on the back of the text (1.674492716 x 10 -24 g)

= 791.88 m/s = 7.92 x 10 2 m/s

Remember: 1 J = 1 kg m 2 /s2


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h

4

(x) (mv) 

The Uncertainty Principle

  • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:

  • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

  • Therefore another broad view of the electron configuration was needed


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6.5 Quantum mechanics and atomic orbitals

  • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.

  • It is known as quantum mechanics.

  • The wave equation is designated with a lower case Greek psi ().

  • The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.


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Quantum Mechanics

  • Electron density distribution in H atom in ground state surrounding the nucleus


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Quantum Numbers

  • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.

  • Each orbital describes a spatial distribution of electron density.

  • An orbital is described by a set of three quantum numbers (____________).


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Principal Quantum Number, n

  • What is n?

  • The values of n are integers ≥ 0 e.g 1, 2, 3 etc.

  • Increase in n means orbital increases too and e- spends more time farther from the nucleus

  • Increase in n also means e- has a higher energy and therefore it is not tightly bound to the nucleus


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Azimuthal Quantum Number, l

  • What is l ? .

  • Allowed values of l are integers ranging from 0 to n − 1.

  • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals e.g. s (sharp), p (principle), d (diffuse), and f (fundamental).



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Magnetic Quantum Number, ml

  • What is ml?

  • Values are integers ranging from -l to l:

    −l ≤ ml≤ l.

  • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.


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Observations

  • Shell with principle quantum n will consist exactly n seashells corresponding to different allowed values of l from 0 to n-1. Example n=1, 1s (l=0); n=2, 2s (l=0), 2p (l =1); n =3, 3s (l=0) 3p (l = 1), 3d (l=2) etc

  • Each subshell consists of specific numbers of orbitals corresponding to different value of ml. For given value of l, there are 2l + 1 allowed ml ranging from -1 to +1. Thus each l=0 consist of one orbital, l =1 (p) consists of three orbitals, l =2 (d) consists of five orbitals, l=3 (f) consists of 7 orbitals etc

  • The total numbers of orbitals in a shell is n2 resulting number of orbitals for the shells of 1, 4, 9, 16 for n= 1, 2, 3 and 4


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Magnetic Quantum Number, ml

  • Orbitals with the same value of n form a shell.

  • Different orbital types within a shell are subshells.


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Practice exercise

  • What is the designation for subshell n = 5 and l = 1?

  • What many orbitals are there in this subshell?

  • Indicate the values of ml for each of these orbitals

(a)

(b)

(c)


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6.6: Representing orbitals

s Orbitals

  • Value of l = 0.

  • Spherical in shape.

  • Radius of sphere increases with increasing value of n.

  • Electron density at any given distance from nucleus is same regardless of direction

  • What makes different s orbitals different?

  • Look at radial electron probability density


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s Orbitals

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.


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s Orbitals


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p Orbitals

  • Value of l = 1.

  • Have two lobes with a node between them

  • Electron density concentrated in two regions on either side of the nucleus

  • Same size and shape but differ in spatial orientation


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d Orbitals

  • Value of l is 2.

  • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.


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6.7 Energies of Orbitals

  • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy.

  • That is, they are degenerate.

  • Example is for Hydrogen atom with one electron

  • What happens in many electron atoms?


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Energies of Orbitals

  • As the number of electrons increases, though, so does the repulsion between them.

  • Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.


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Spin Quantum Number, ms

  • In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.

  • The “spin” of an electron describes its magnetic field, which affects its energy.


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Spin Quantum Number, ms

  • What is ms ?

  • What are the allowed values?


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Pauli Exclusion Principle

  • What is this principle?_________________________

  • _________________________________

  • This also unlocks the understanding of the structure of the periodic table of the elements

  • For example, no two electrons in the same atom can have identical sets of quantum numbers.


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6.8 Electron Configurations

This is the way the electrons are distributed among the various orbitals in the atoms

Lowest possible energy state: ground state

Without restrictions all electrons will crowd in the ground state

Orbitals are filled with increasing energy with no than two electrons per orbital

  • Distribution of all electrons in an atom

  • Consist of

    • Number denoting ____________


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Electron Configurations

  • Distribution of all electrons in an atom

  • Consist of

    • Number denoting the energy level

    • Letter denoting the ____________


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Electron Configurations

  • Distribution of all electrons in an atom.

  • Consist of

    • Number denoting the energy level.

    • Letter denoting the type of orbital.

    • Superscript denoting the _______________________________


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Orbital Diagrams

  • Each box represents one orbital.

  • Half-arrows represent the electrons.

  • The direction of the arrow represents the spin of the electron.


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Hund’s Rule

  • “What does it say?___________________________

  • _________________________________________

  • This is based on electron repulsion. By occupying different orbitals, the electrons remain away from each other.


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Practice exercise

(a)Write the electron configuration for phosphorus, element 15.

(b) How many unpaired electron does a phosphorus atom posses?

(c) What do you think are valence electrons?


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Condensed Electron Configuration

How is this done?_________________________

e.g. Give an example here for Na


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Important terminologies

  • What are Core electrons?_____________________________

    e.g. 1s2, 2s2, 2p6in Na

    What are outer shell electrons?_________________________

    e.g. 3s1in Na

  • Outshell electrons involved in chemical bonding are called

  • _________________________________

  • For elements with atomic number 30 or less, all outer shell electrons are valence electrons

  • Many heavier elements, completely filled subshells are not involved in bonding, therefore not valence electrons


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Transition metals

  • These occupy first 4s before 3d, this is because 4s is less in energy than 3d e.g. K [Ar] 4s1

  • Scandium to Zinc electrons go to 3d

  • 4th row is ten elements wider than previous ones and are called transitional elements or transitional metals

  • Note position of these and filling of orbitals follows Hund’s rule

  • Condensed form e.g. Mn [Ar] 4s2 3d5

  • Once 3d is filled, 4p starts

  • In Krypton, Z=36, 4s and 4p completely filled


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Lanthanides and Actinides

  • Elements 57-70 are placed below the main portion of the table

  • 4f orbitals are encountered with 7 allowed ml values ranging from 3 to -3.

  • Elements filling the 4f are called lanthanide elements or the rare earth elements and have similar properties.

  • 4f and 5d have close energies some lanthanide electron configuration involve 5d e.g.

    Lanthanide [Xe] 6s2 5d1, Cerium [Xe] 6s2 5d1 4f1

  • Final row begins filling the 7s . The actinides then follow filling the 5f orbitals. Most of these are radio active.


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Periodic Table

  • We fill orbitals in increasing order of energy.

  • Different blocks on the periodic table, then correspond to different types of orbitals.


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Some Anomalies

Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.


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Some Anomalies

For instance, the electron configuration for copper is

[Ar] 4s1 3d5

rather than the expected

[Ar] 4s2 3d4.


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Some Anomalies

  • Explain the anomaly for copper.__________________

  • _________________________________________

  • These anomalies occur in f-block atoms, as well.


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Typical questions

1. Consider the system of orbitals arranged in order of increasing energy and identified by principal quantum number. Which of the following electron transitions corresponds to emission of electromagnetic radiation having the longest wavelength?

  • n = 2 to n = 1

  • n= 1 to n = 2

  • n = 6 to n = 1

  • n = 1 to n = 6

  • n = 6 to n = 5

n

6

5

4

3

2

1


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Typical questions

2. The valence electron configuration of an atom of an element X is 3s2 3p1 and that of an atom Y is 3s23p4. What would be the probable empirical formula for a compound of the two elements?

  • X2Y

  • XY2

  • X3Y2

  • X2Y3

  • XY


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Typical questions

3. The position of four lines of the visible line spectrum of the hydrogen atom are shown below. Two lines are violet, one is red and the other is blue. Which of the following statements describes the spectrum correctly?

H

650

600

550

500

450

400 nm

The lines with high energy transitions are shown to the right

The red line is shown between 450 and 500 nm

Lines with small wavelength are associated with radiation of high frequency

a. All are correct, b. 2 and 3 c. 1 and 3 d. 1 and 2, e.only 3


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Typical questions

4. Suppose an atom has six energy levels. What would be the maximum number of lines in its emission spectrum?

  • 6

  • 12

  • 15

  • 21

  • 24

n

6

5

4

3

2

1


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