Lecture notes, Atomic Structure Week 1 PDF

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For the next two weeks we’ll look at ATOMIC & MOLECULAR STRUCTURE SUMMARY OF TEXTBOOK SECTIONS: Chapter 7: 7.1 – 7.5 (Note that sections 7.1-7.4 are for you to review.)  Characteristics of light, quanta and photons.  Atomic spectra and energy levels.  Schrödinger and quantum numbers

Chapter 8 & 9: 8.1 – 8.7, 9.2 – 9.5  Electron spin and electron configurations  Periodic properties and bonding

Chapter 9: 9.6 – 9.9  Lewis structures for molecules and ions.  Formal charges and resonance.  Octet Rule

Chapter 10 & 11: 10.1 – 10.4 & 11.5  Molecular shape and polarity (Refer to on-line VSEPR Interactive Tutorial)  Hybridisation  Intermolecular forces

***************************************************************************** Beginning of Review

***************************************************************************** THINGS YOU SHOULD KNOW …

Light, Spectroscopy & Structure of Atoms Early 19th Century: • Chemistry was a purely descriptive science. • Reactions and properties observed and recorded – little understanding Late 19th Century: • Systematic behaviour of the elements is revealed but not understood. • Mendeleev/Meyers & Periodic Table: elements arranged in order of atomic number fall into "groups" of related properties. Important clues to the structure of atoms & matter came from the study of the emission of light by atoms and molecules – which lead to the 20th century science of SPECTROSCOPY. NOTE:

Spectroscopy is the study of spectra, i.e., the dependence of a physical measure to frequency. Spectroscopy is heavily used in astronomy. Spectroscopy is also often used in physical and analytical chemistry for the identification of substances, through the spectrum emitted or absorbed. A device for recording a spectrum is a “spectrometer”.

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SIMPLE HYDROGEN EMISSION SPECTROSCOPY EXPERIMENT:

Reference: http://xenon.che.ilstu.edu/genchemhelphomepage/topicreview/bp/ch6/bohr.html

In the spectrum of the simplest atom hydrogen (see above) how do we explain the lines? Why isn’t the spectrum continuous? Can we extend our ideas to more complex atoms and molecules? Refer to Figure 7.2 in our text for the emission (line) spectra for other elements.

THE ELECTROMAGNETIC SPECTRUM

Reference: http://acept.la.asu.edu/PiN/rdg/color/color.shtml

(Refer to Figure 7.5 in text for coloured version of the visible spectrum.) ♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦

For Your General Interest: Radio waves are very long compared to the rest of the electromagnetic spectrum. The radio spectrum is divided up into a number of "bands" based on their wavelength and usability for communication purposes. They extend from the Very Low Frequency portion of the spectrum through the Low, Medium, High, Very High, Ultra High, and Super High to the Extra High Frequency range as depicted in the illustration below. Above the EHF band comes infrared radiation and then visible light.

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Band VLF LF MF HF

Frequency 3 - 30 kHz 30 - 300 kHz 300 kHz - 3 MHz 3 - 30 MHz

Wavelength 100 km - 10 km 10 km - 1 km 1 km - 100 m 100 m - 10 m

Some Uses Long range navigation and marine radio Aeronautical and marine navigation AM radio and radio telecommunication Amateur radio bands, NRC time signal

VHF UHF SHF EHF

30 - 300 MHz 300 MHz - 3 GHz 3 - 30 GHz 30 - 300 GHz

10 m - 1 m 1 m - 10 cm 10 cm - 1 cm 1 cm - 1 mm

TV, FM, cordless phones, air traffic control UHF TV, satellite, air traffic radar, etc Mostly satellite TV and other satellites Remote sensing and other satellites

Reference: http://members.shaw.ca/weskyscan/the_electromagnetic_spectrum.htm ♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦♦

LIGHT:  a type of electromagnetic radiation (refer to Figure 7-5, page 268 in text).  fluctuating electric and magnetic fields

References:

http://www.astronomynotes.com by Nick Strobel Silberberg, M., Chemistry: The Molecular Nature of Matter & Change. 3rd ed. (McGraw-Hill Company, Inc., New York, 2003).



 described by a Wavelength, λ (lambda) and a Frequency ν (nu) (You may have seen frequency defined as “f” in another class.)

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Reference: http://acept.la.asu.edu/PiN/rdg/color/color.shtml

The wavelength and the frequency are related by: c = λ × ν where "c" is the velocity of light = 3.00×108 ms–1 in a vacuum. Units: c → m s–1, λ → m, ν → s–1 NOTE: The unit s–1 = 1/s = reciprocal time = "per second" is given the special name hertz, abbreviated Hz (1 Hz = 1 s–1) Example 1: What is the frequency of yellow light of wavelength 625 nm? Think: Use ν = c / λ (watch units) The prefix "n" means "nano" = 1× 10–9 m, therefore, 625 nm = ν=c/λ ν= ν=

Example 2: Our University Radio Station CFRU broadcast at a frequency of 93.3 MHz. What would be the wavelength of the radio wave in metres? (Ans: 3.22 m)

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19th century physicists could not explain the wavelength distribution of light emitted by heated objects (i.e. black-body radiation). Examples include electric elements on stoves or filaments in light bulbs.

Reference: Silberberg, M., Chemistry: The Molecular Nature of Matter and Change. 3rd ed. (McGraw-Hill Company, Inc., New York, 2003).

The amount and type of electromagnetic radiation that is emitted is directly proportional to temperature. Black bodies below ~700 K (426.85 ºC) produce very little radiation at visible wavelengths and appear black (hence the name). Black bodies above this temperature, however, begin to produce radiation at visible wavelengths starting at red, going through orange, yellow, and white before ending up at blue as the temperature increases.

Max Planck proposed that electromagnetic radiation comes in units of defined energy, rather than in any arbitrary quantities. Planck called the unit of light energy the quantum. He was able to determine the following relationship:

ε=h×ν where "h" is a universal constant known as Planck's constant (h = 6.63 × 10–34 J s) This was revolutionary and marked a turning point in the history of physics. Its importance was not initially realised, but evidence gradually showed how it explained many discrepancies between observed phenomenon and classical theory, for example Einstein’s explanation of the photoelectric effect (refer to pg 270 & Figure 7.6 in text). Planck won the Nobel Prize in Physics in 1918. (Reference: http://nobelprize.org/physics/laureates/1918/planck-bio.html)

Demonstration of the Photoelectric Effect (refer to page 270 in text)

Reference: Silberberg, M., Chemistry: The Molecular Nature of Matter and Change. 3rd ed. (McGraw-Hill Company, Inc., New York, 2003).

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Example 3: Determine the energy of red light at 650 nm. (show yourselves that this light corresponds to a frequency of 4.62×1014 s–1)

ε=h×ν= ε=

6.63x10^-34 Js x 3x10^8 m/s / 650x10^-9 m

(Ans: 3.1 ×10–19 J)

= 3.1 * 10^-19 h * c/frequency For 1 MOLE of QUANTA, we have E = NA × ε E = 6.022×1023 photons/mole × 3.1 ×10–19 J = 190000 or 190 kJ/mol N.B. Low frequency light gives rise to small quanta and high frequency light gives rise to large quanta (in energy terms).

After Planck, quantization of light and emission spectra lead to the Bohr model of the atom (or "planetary model"). (Reference: http://csep10.phys.utk.edu/astr162/lect/light/bohr.html)

Excitation by absorption of light (or energy) and de-excitation by emission of light:

Reference: http://www.cartage.org.lb/en/themes/Sciences/Astronomy/Modenastronomy/Interactionoflight/TheBohrModel/TheBohrModel.htm

The movement of electrons from one orbital to another required absorption or emission of quantised energy. This explained the H spectra. 6

The DEVELOPMENT of the THEORY of ATOMIC STRUCTURE While studying at the University of Paris, Louis de Broglie was influenced by both relativity and the photoelectric effect. The photoelectric effect indicated that light, which was thought to be a wave, also expressed particle properties. He wondered if electrons and other "particles" might then also exhibit wave properties. de Broglie later introduced the relationship between momentum and wavelength of matter (λ = h/mv). He found that indeed matter exhibits wave properties as well as particle properties. de Broglie also suggested that an electron in an atom must have an orbital with a circumference equal to a whole number multiple of the wavelength. In 1929 the Swedish Academy of Sciences conferred on him the Nobel Prize for Physics "for his discovery of the wave nature of electrons". (Ref: http://nobelprize.org/physics/laureates/1929/broglie-bio.html)

In 1910, Ernest Rutherford postulated the concept of a "nucleus" based on the scattering of alpha rays. He proposed that the entire mass of the atom and all its positive charge was concentrated in a minute space at the centre. When studying atoms, he expected that classical mechanics could be used, but quickly found that it did not. (Reference: http://nobelprize.org/chemistry/laureates/1908/rutherford-bio.html)

A new approach was needed. This lead to the creation of quantum mechanics. In 1912, Niels Bohr joined Rutherford and he adapted Rutherford's nuclear structure to work with Max Planck's quantum theory to obtain a theory of atomic structure. This theory was later improved as a result of Heisenberg's uncertainty principle but still remains valid to this day. (Reference: http://nobelprize.org/nobel_prizes/physics/laureates/1922/index.html) In 1926, Erwin Schrödinger set out the general equations describing wave motion for atoms (and won the Nobel Prize in Physics in 1933). The equations are complex (beyond the scope of this course) but their solutions are importance to us. The wave function (ψ) describes the amplitude of an electron wave at any point in space. The square of the wave function (ψ2) gives the probability of finding the electron at any point in space. Reference: http://nobelprize.org/physics/laureates/1933/schrodinger-bio.html

Three quantities (n, ℓ, mℓ) called quantum numbers are involved in the wave equations. There are many solutions to the wave function. Each is characterized by a set of quantum numbers. Each quantum number can have many integral values and each set yield one solution to the wave equation. A specific set of values for n, ℓ and mℓ, corresponds to an electron ORBITAL. For H, n = 1, ℓ = 0, mℓ = 0 describes the energy of the electron in the GROUND STATE. An electron orbital defines the energy and spatial characteristics of the electron. The Wave Mechanical Model of the atom differs from the earlier Bohr model in certain respects. Gone are fixed orbits, which are now replace by probability distributions. The Wave Mechanical Model is a three dimensional model. The electron distribution for the hydrogen atom is found as a spherical distribution around the nucleus. Refer to Figure 7.19 for the probability density plot.

***************************************************************************** End of Review

**************************************************************************** 7

Quantum Numbers (refer to section 7.5 in text, p. 282): PRINCIPAL Quantum Number, n •

NOTES:

represents the ________________________ of an atom's electrons by a energy number n: Letter code:

1, 2, 3, 4, … , etc. K, L, M, N, … , etc. (used in spectroscopy)

• a K-Shell electron is an electron in the shell with quantum number n = 1 • increasing values of n corresponds to _________________ increasing values of energy for the electron • permitted values of n are 1, 2, 3, 4, ..., etc. (by integers) ANGULAR MOMENTUM (or Azimuthal) Quantum Number, ℓ

shape • tells us about the _______________ of the electron cloud or orbital • particular electron cloud shapes are associated with particular values of ℓ ℓ = 0, spherical ℓ = 1, dumb-bell shaped ℓ = 2, a variety of shapes – 5 in all.

Reference: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/quantum.html#shells

(Also refer to Figures 7.24 to 7.27 in text.) • both number and letter codes are used ℓ: 0, 1, 2, 3, … , etc. Letter code: s, p, d, f, … , etc. • permitted values of ℓ are from 0 to (n – 1)  if n = 1, ℓ = 0  if n = 2, ℓ = 0 or 1  if n = 3, ℓ = 0 or 1 or 2  if n = 4, ℓ = 0 or 1 or 2 or 3 MAGNETIC Quantum Number, mℓ

number • determines the __________________ of permitted orbitals in any group • permitted mℓ values range from –ℓ through zero to +ℓ  if ℓ = 0, mℓ = 0 8

 if ℓ = 1, mℓ = –1, 0, or +1



NOTES:

if ℓ = 2, mℓ = –2, –1, 0, +1 or +2

orientation in space of an electron cloud. • mℓ specifies the permitted __________________ • tells you how many orbital(s) exist in a sub–levels based on the ℓ value. Refer to Table 7.1 for permissible values of quantum number for atomic orbitals. SPIN Quantum Number, ms • this quantum number does NOT arise from the Schrödinger equations (Refer to Figure 8.2 – Stern-Gerlach Experiment.)

+/- 0.5 • limits the number of spin energies for an electron to two values: _____________. Summary of Allowed Combinations of Quantum Numbers Number of Electrons Needed to Fill Subshell 2

Total Number of Electrons in Subshell (2n2) 2 8

Shell

n

ℓ

mℓ

Subshell Notation

K

1

0

0

1s

Number of Orbitals in the Subshell 1

L

2 2 3 3 3

0 1

0 +1,0, –1

2s 2p

1 3

2 6

0 1 2

0 +1,0,–1 ±2, ±1,0

3s 3p 3d

1 3 5

2 6 10

0 1 2 3

0 +1,0, –1 ±2, ±1,0 ±3, ±2, ±1, 0

4s 4p 4d 4f

1 3 5 7

2 6 10 14

M

N

4 4 4 4

18

32

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Electronic Structure of The Elements Each electron is represented by a set of 4 quantum numbers: NOTES: n: main energy level; relative distance of the electron from the nucleus. ℓ: sub-shell & shape of electron cloud. Each orbital of a sub-shell is identical in energy. mℓ: designates the orientation of the orbital in space and also tells you how many orbitals. ms: spin of the electron – only two options You can envisage a set of n, ℓ, mℓ and ms as a unique electron address, specifying the shape, energy and orientation cloud and the spin of the electron.

Pauli exclusion Principal:

identical No two electrons can have the _________________ sets of all four quantum numbers (three may be the same, but then the fourth MUST be different. Hund's Rule of Maximum Multiplicity: Electrons are distributed in among the orbitals of a sub–shell in such a way unpaired electrons as to yield the maximum number of _______________________________. A set of n, ℓ and m ℓ specifies an ORBITAL, which can contain up to two electrons  when an orbital is full (i.e., contains 2 electrons with quantum numbers ms equal to +½ and –½), we call this "_______________________"; spin paired  when an orbital contains only one electron, we say this is "_____________________". unpaired In general, electrons in orbitals with different values of ℓ, i.e., in different sub-levels, have different energies which increase with ℓ–value, i.e., ℓ = 0 < ℓ = 1 < ℓ = 2 < ℓ = 3 s < p < d < f

The nℓx notation: e.g. 1s2 (2 electrons in shell with n=1 & ℓ=0), 2s1, 3d7, … We are now in the position to arrive at the electronic structure of the elements, making use of the AUFBAU principal developed by Pauli. (Building-up Principle).  hypothetical process where electron structure is correctly deduced by successive addition of the electrons, _______________________. one at a time until no  need to obey Hund’s Rule  orbitals arranged in order of ____________________ energy increasing  continue until no more electrons left.

more remain

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lowest

We assume that each electron occupies the _______________ energy level available to it, and since all electron orbitals of a given sub-level have __________________energies, this amounts to an arrangement by energy equal sub-level.

NOTES:

Complication: It is possible, and indeed happens, for a simple orbital of one level (e.g., 4s) to have a lower energy than a more complicated orbital of a previous level (e.g., 3d), and hence the 3d energy level is filled after the 4s fills. Note that the AUFBAU principal is a generalisation.

Reference: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/quantum.html#shells

Refer to Figure 8.12 for a periodic table illustrating the building-up order, p. 308. 11

highest Valence Shell: Those orbital(s) in an atom of the _________________ occupied principal level (n) and the orbital(s) of partially filled sub-levels of the lower principal quantum number.

NOTES:

Valence Electrons are those that occupy the _______________________ orbital(s). All other electrons not in the valence shell are core electrons

Examples: Element

Electron Configuration

He

Atomic Number (Z) 2

1s2

↑↓ __

__ __ __

Li

3

1s22s1 OR [He]2s1

↑↓ ↑_

__ __ __

Be

4

1s22s2 OR [He]2s2

↑↓ ↑↓

__ __ __

B

5

[He]2s22p1

[He] ↑↓

↑_ __ __

C

6

[He] ↑↓

__ __ __

N

7

[He] ↑↓

__ __ __

O

8

[He] ↑↓

__ __ __

F

9

[He] ↑↓

__ __ __

Ne

10

[He] ↑↓

__ __ __

Orbital Representation 1s 2s 2p

For transition metal species the d-shell and s-shell are very close in energy. Once we start filling the d-shell, this stabilizes the shell and it decreases in energy, enough so that it falls below the s-shell, i.e., we have 3d14s2 NOT 4s23d1. Element Atomic Number (Z)

Electron Configuration

Orbital Representation

V

23

Fe

26

[Ar] 4s2 3d3 = 3d3 4s2 [Ar] 4s2 3d6 = 3d6 4s2

Co

27

[Ar] 4s2 3d4 = 3d5 4s1

Cr

24

Cu

29 12

When writing the electron configurations for ions., first start with the neutral atom

NOTES:

and then adjust the amount of electrons according to the charge of the ion. e.g., Na+ Na

1s2

2s2

↑↓

↑↓

1s2

2s2

↑↓

↑↓

↑↓

2p6

3s1

↑↓ ↑↓

↑_

Na+

e.g., Cl– Cl

2p5 ↑↓

↑↓ ↑_

e.g., Fe2+ Fe

[Ar]

3d6

4s2

[Ar]

↑↓ ↑_ ↑_ ↑_ ↑_

↑↓

Magnetic Properties:

not attracted or slightly repelled

1. diamagnetism: ____________________________ by magnetic fields

into 2. paramagnetism: drawn ________________ by magnetic fields magnet ♦ A single electron behaves like a small _________________________. ♦ Two paired electrons in an orbital, have opposed spins & their magnetic